Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at |x − (−1)| = x + = ±3 x=2 −4 x = −4 | − − 2| = | − 7| = |2 − 7| = | − 5| = | − − 7| = | − 12| = 12 2x − = ±6 2x = 10 x=5 2x = −2 x = −1 x − = ±2 2x + = ±5 x=5 2x = x=1 x=1 2x = −8 x = −4 −2 Full file at Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at ± (2x + 4) = ± (5x − 2) = 5x − 2x + 2x + = − (5x − 2) x=2 x = − 27 − 3u = ± (3 + 2u) − 3u = + 2u u= − 3u = −3 − 2u u=8 4+ t =± 2t −2 t=6 t = −1 2s − = ± (7 − s) s= 10 s = −4 −4 ≤ 5x − ≤ −4 + ≤ 5x ≤ + 2 − ≤x≤ 5 − 3x < −8 < 3x − 3x > −3x > x>3 x < − 73 7x + ≥ 7x + ≤ −3 x ≥ − 17 7x ≤ −7 x ≤ −1 |6 − 5x| < −7 < − 5x < −7 − < −5x < − −13 < −5x < − 15 < x < Full file at 13 Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall −3 Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at −6 < 2x + < −9 < 2x < 3 − 4x ≥ x≥ − 92 < x < − 4x ≤ −2 x≤ −1 ≤ x + ≤ −6 ≤ x ≤ −4 x y − y0 = m(x − x0 ) y − = − 13 (x − 2) 3(y − 4) = −(x − 2) 3y − 12 = −x + x + 3y − 14 = (x0 , y0 ) = (1, −2) m = y − y0 = m(x − x0 ) y − (−2) = 2(x − 1) y + = 2x − y − 2x + + = −2x + y + = A = −2 B = C = 2x − y − = A = B = −1 C = −4 (x0 , y0 ) = (0, −2) m = −3 y − y0 = m(x − x0 ) y − (−2) = −3(x − 0) y + = −3x 3x + y + = (x0 , y0 ) = (−3, 5) m = A=3 B=1 C=2 y − y0 = m(x − x0 ) y − = 12 (x − (−3)) y − = 12 (x + 3) 2(y − 5) = x + 2y − 10 = x + Full file at Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at −x − + 2y − 10 = −x + 2y − 13 = A = −1 B = C = −13 x − 2y + 13 = A = B = −2 C = 13 (x, y1 ) = (−2, −3) (x2 , y2 ) = (1, 4) m= y2 −y1 x2 −x1 m= = (4)−(−3) (1)−(−2) = 4+3 1+2 y − y0 = m(x − x0 ) (x0 , y0 ) (x1 , y1 ) (x2 , y2 ) y − = 73 (x − 1) 3(y − 4) = 7(x − 1) 3y − 12 = 7x − 3y − 7x − 12 + = −7x + 3y − = 7x − 3y + = (x1 , y1 ) = (−1, 4) m= m= y2 −y1 x2 −x1 − 12 − 82 = = (x2 , y2 ) = (2, − 12 ) (− 12 )−(4) − 12 −4 (2)−(−1) = − 92 −9 −3 = · = y − y0 = m(x − x0 ) y − (4) = − 32 (x − (−1)) y − = − 32 (x + 1) 2(y − 4) = −3(x + 1) 2y − = −3x − 3x + 2y − = A = B = C = −5 (x1 , y1 ) = (0, 4) (x2 , y2 ) = (3, 0) m= Full file at y2 −y1 x2 −x1 = (0)−(4) (3)−(0) = − 43 Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at y − y0 = m(x − x0 ) y − = − 43 (x − 0) 3(y − 4) = −4x 3y − 12 = −4x 4x + 3y − 12 = (x1 , y1 ) = (1, −1) m= y2 −y1 x2 −x1 = (5)−(−1) (4)−(1) = (x2 , y2 ) = (4, 5) =2 y − y0 = m(x − x0 ) y − = 2(x − 4) y − = 2x − −2x + y + = 2x − y − = y=k (3, 32 ) y= 2y − = y=k (0, −1) y = −1 y+1=0 x = h (−1, 72 ) x = −1 x+1=0 x = h (2, −3) x = x−2=0 m=3 y (0, 2) 3x − y + = y = 3x + m = −1 y (0, −3) y = mx + b y = −1x − m= x+y+3=0 y (0, 2) y = mx + b y = 12 x + x − 2y + m = − 13 y (0, −1) y = mx + b Full file at Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall y = mx + b Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at y = − 13 x − x + 3y + = m = −2 x (1, 0) y − y0 = m(x − x0 ) y − = −2(x − 1) y = −2x + 2x + y − = m=1 x (−2, 0) y − y0 = m(x − x0 ) y − = 1(x − (−2)) y =x+2 −x + y − = x−y+2=0 m = − 14 x (3, 0) y − y0 = m(x − x0 ) y − = − 14 (x − 3) y = − 14 x + x + 4y − = m= x (− 12 , 0) y − y0 = m(x − x0 ) y − = 15 (x − (− 12 )) y = 15 (x + 12 ) y = 15 x + 10 2x − 10y + = (2, −3) x + 2y − = x + 2y − = x + 2y − = 2y − = −x 2y = −x + 2y = −x+4 y = − 12 x + Full file at m = − 12 Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at m = − 12 (2, −3) y − y0 = m(x − x0 ) y − (−3) = − 12 (x − 2) y + = − 12 (x − 2) y + = − 12 x + 2(y + 3) = (− 12 x + 1)2 2y + = −x + x + 2y − = x + 2y + = (2, −3) x − 3y − = (1, 2) x − 3y − = −3y − = −x −3y = −x + y= −x+6 −3 y = 13 x − m= y − y0 = m(x − x0 ) (1, 2) y − = 13 (x − 1) 3y − = x − −x + 3y − + = −x + 3y − = x − 3y + = (−1, −1) m= m= (0)−(1) (3)−(0) (0, 1) y2 −y1 x2 −x1 = − 13 y − y0 = m(x − x0 ) y − (−1) = − 13 (x − (−1)) y + = − 13 (x + 1) −3(y + 1) = x + −3y − = x + Full file at Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall (3, 0) Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at x + 3y + = (2, −3) m= y2 −y1 x2 −x1 m= 2 = (0, −1) (1)−(−1) (2)−(0) =1 y − y0 = m(x − x0 ) (2, −3) y − (−3) = 1(x − 2) y+3=x−2 −x + y + + = −x + y + = x−y−5=0 (1, 4) 2y − 5x + = 2y − 5x + = 2y = 5x − 2y = 5x−7 y = 52 x − m= m⊥ = − m m⊥ = −1 ( 52 ) m1 · m2 = −1) = − 25 (1, 4) y − y0 = m⊥ (x − x0 ) y − = − 25 (x − 1) 5(y − 4) = −2(x − 1) 5y − 20 = −2x + 2x − + 5y − 20 = 2x + 5y − 22 = (−1, −1) x−y+3=0 x−y+3=0 −y = −x − y =x+3 m=1 Full file at m1 · m2 = −1 Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall (2, 1) Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at m⊥ = − m = − 11 = −1 (−1, −1) y − y0 = m⊥ (x − x0 ) y − (−1) = −1(x − (−1)) y + = −(x + 1) y + = −x − y = −x − − y = −x − x+y+2=0 (5, −1) m= y2 −y1 x2 −x1 = (−2)−(1) (1)−(−2) (−2, 1) (1, −2) = − 33 m = −1 m⊥ = − m = −1 −1 =1 (5, −1) y − y0 = m⊥ (x − x0 ) y − (−1) = 1(x − 5) y+1=x−5 y =x−6 x−y−6=0 (4, −1) (1, 1) m= y2 −y1 x2 −x1 m⊥ = −1 ( 13 ) = (1)−(0) (1)−(−2) = = −3 (4, −1) y − y0 = m⊥ (x − x0 ) y − (−1) = −3(x − (4)) y + = −3(x − 4) y + = −3x + 12 y = −3x + 11 3x + y − 11 = Full file at Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall (−2, 0) Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at (4, 2) y=2 y−2=0 (−1, 5) y−5=0 y=5 x = −1 x+1=0 x=3 x−3=0 x=1 x−1=0 x=4 x−4=0 y=3 y−3=0 y=5 y−5=0 y = 30.5x y = mx y x x m x y y = 30.5x x = y = 30.5(6) = 183 y = 30.5x x = 2 12 ≈ 0.167 x = 3.167 y = 30.5(3.167) = 96.58 y = 30.5x x = Full file at = 12 ≈ 0.583 Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall y Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at https://TestbankDirect.eu/ sin2 θ cos2 θ + cos2 θ cos2 θ = cos2 θ sin θ = tan θ, cos θ = sec θ cos θ tan2 θ + = sec2 θ sin2 θ + cos2 θ sin2 θ + cos2 θ = sin2 θ sin2 θ cos2 θ + sin2 θ sin2 θ =1 sin2 θ sin2 θ = sin2 θ cos θ = cot θ, sin θ = csc θ sin θ + cot2 θ = csc2 θ cos θ sin θ cos θ sin θ = sin θ cos θ = sin θ, sin θ sin θ [0, 2π) sin θ = θ=0 θ=π =1 cos θ = θ= π θ = 0, π, 2π − π π π Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Full file at https://TestbankDirect.eu/ Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at https://TestbankDirect.eu/ sec2 x = √ sec2 x = + tan2 x tan x + 1 + tan2 x = tan2 x tan x · tan x = tan x tan x x = 0, π3 √ · tan x + √ = tan x √ 3·tan x tan x tan x = = √ 3, x= π x=0 π + π3 3π 43 4−2/3 ar as = ar+s √ 43+(−2/3) = 47/3 = 16 32 31/2 3−1/2 = 35/2 3−1/2 = 35/2 · 31/2 = 35/2+1/2 = 36/2 = 33 = 27 5k 52k−1 51−k 5k+2k−1+k−1 = 5k · 52k−1 · 5k−1 = 54k−2 Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Full file at https://TestbankDirect.eu/ Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at https://TestbankDirect.eu/ (24 · 2−3/2 )2 (28/2 · 2−3/2 )2 (28/2−3/2 )2 (25/2 )2 = 25 = 32 65/2 · 62/3 61/3 = = 65/2+2/3 61/3 = 619/6 62/6 615/6+4/6 62/6 3 = 6(19/6)−(2/6) = (617/6 )3 = 6(17/6)·3 = 617/2 3−2k+3 34+k 3−3k−1 = 3−2k+3−4−k = 3(−3k−1)(3) = 3−9k−3 , 33(−3k−1) = 33 −3k−1 = 27−3k−1 = −2 log4 x x = 4−2 = 42 = 16 = −3 log1/3 x x = −3 = ( 13 ) = 1 ( 27 ) = 27 Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Full file at https://TestbankDirect.eu/ Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at https://TestbankDirect.eu/ = −2 log10 x x = 10−2 = 102 = 100 log1/2 x = −4 x= −4 = 1−4 = 2−4 = 24 1 16 = 16 log1/4 x = x= log5 x = 12 1 = = 44 16 16 = x = 53 = 125 log1/2 32 32 = =x x = 1x 2x 2x = 2x = 2−5 x = −5 log1/3 81 81 3x = x = 2x 32 =x = 81 x = 34 = 1x 3x = 3−4 = −4 Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Full file at https://TestbankDirect.eu/ Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at https://TestbankDirect.eu/ log10 0.001 =x 10x = 0.001 = 1000 = 103 = 10−3 10x = −3 x log4 64 =x 64 = 4x 43 = 4x x =3 log1/5 625 =x 625 = x 54 = (5−1 )x 54 = 5−x −x =4 = −4 x log10 10, 000 =x 10, 000 = 10x 104 = 10x x =4 Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Full file at https://TestbankDirect.eu/ Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at https://TestbankDirect.eu/ − ln = ln −1 = ln log4 (x2 − 4) = log4 [(x − 2)(x + 2)] = log4 (x − 2) + log4 (x + 2) log2 4(3x−1) = (3x − 1) log2 (22 ) = (3x − 1)(2 · log2 2) = (3x − 1)(2 · 1) = 6x − − ln ln = ln x2√ −y x −1 = ln = ln(x − y) + ln(x + y) − ln(x1/2 ) = ln(x − y) + ln(x + y) − 12 ln x log3 32x+1 = (2x + 1)(log3 3) = 2x + e3x−1 =2 ln e(3x−1) = ln (3x − 1)(ln e) = ln ln e = 3x − = ln 3x = + ln x = e−2x 1+ln = 10 ln e(−2x) = ln 10 (−2x)(ln e) = ln 10 −2x = ln 10 x = ln 10 −2 = − 12 · ln 10 x = ln 10−1/2 = ln √1 10 Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Full file at https://TestbankDirect.eu/ Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at https://TestbankDirect.eu/ ex ln e(x −1 = 10 −1) = ln 10 (x2 − 1)(ln e) = ln 10 x2 − (ln e = 1) = ln 10 x2 = + ln 10 √ = ± + ln 10 x 3x = 81 3x = 34 x =4 92x+1 = 27 (32 )(2x+1) = 33 3(2)(2x+1) = 33 2(2x + 1) =3 4x + =3 4x =1 x = 105x = 1000 105x 5x x = 103 =3 = Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Full file at https://TestbankDirect.eu/ Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at https://TestbankDirect.eu/ ln(x − 3) =5 eln(x−3) = e5 , x−3 x eln x = x = e5 = e5 + ln(x + 2) + ln(x − 2) =1 ln(x + 2)(x − 2) =1 eln[(x+2)(x−2)] =e (x + 2)(x − 2) =e x2 − =e x2 =4+e √ x = 4+e log3 x2 − log3 2x = x2 log3 =2 2x x2 = 32 2x x =9 x = 18 ln(2x − 3) =0 Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Full file at https://TestbankDirect.eu/ Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at https://TestbankDirect.eu/ eln(2x−3) = e0 , eln x = x 2x − =1 2x =4 x =2 log2 (1 − x) =3 2log2 (1−x) = 23 1−x =8 x = −7 ln x3 − ln x2 = x3 ln = x ln x = x =e − 2i − (−2 + 5i) = − 2i + − 5i = − 7i (7 + i) − = − + i = + i (4 − 2i) + (9 + 4i) = + − 2i + 4i = 13 + 2i (6 − 4i) + (2 + 5i) = + − 4i + 5i = + i 3(5 + 3i) = 15 + 9i (2 − 3i)(5 + 2i) = · + · 2i − · 5i − 6i2 = 10 + 4i − 15i − 6(−1) i2 = −1 = 10 + 4i − 15i + = 16 − 11i Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Full file at https://TestbankDirect.eu/ Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at https://TestbankDirect.eu/ (6 − i)(6 + i) = 36 − i2 = 36 − (−1) = 37 (−4 − 3i)(4 + 2i) = −4 · − · 2i − 3i · − 6i2 i2 = −1 = −16 − 8i − 12i − 6(−1) = −16 − 20i + = −10 − 20i z = − 2i z = + 2i z + u = (3 − 2i) + (−4 + 3i) = − 2i − + 3i = −1 + i z + v = − 2i + + 5i = + 2i + − 5i = − 3i v − w = + 5i − (1 − i) = − 5i − (1 + i) = − 5i − − i = − 6i vw = (3 + 5i)(1 − i) = + 2i = − 2i uz = (−4 + 3i)(3 − 2i) = −6 + 17i = −6 − 17i z z+z = a + bi = a + bi + a + bi = a + bi + a − bi = 2a Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Full file at https://TestbankDirect.eu/ Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at https://TestbankDirect.eu/ z−z = (a + bi) − (a + bi) = a + bi − (a − bi) = a + bi − a + bi = 2bi z = a − bi z = a + bi (z) = (a − bi) = a + bi = z z = (z) 2x2 − 3x + = a = b = −3 c = x1,2 = x1,2 = i2 = −1 √ ab = √ a· √ = b x1,2 x1 = √ (−3)2 −4(2)(2) 2(2) √ = 3± 49−16 √ √ 3± −7 = 3± 7i −(−3)± x1,2 x1,2 √ −b± b2 −4ac 2a = √ √ 3± 7· i2 √ 3+ 7i = √ 3± 7i x2 = √ 3− 7i a = b = −2 c = x1,2 x1,2 = x1,2 x1,2 x1,2 x1,2 = √ −b± b2 −4ac 2a √ (−2)2 −4(3)(1) 2(3) √ 2± 4−12 = √ = 2± −8 √ = 2±6 8i √ = 2±22·3 2·i −(−2)± Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Full file at https://TestbankDirect.eu/ Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at https://TestbankDirect.eu/ x1,2 = x1 = x2 = a = −1, b = √ 1± 2·i √ 1+ 2i √ 1− 2i c=2 = x1,2 x1,2 x1 x2 √ (1)2 −4(−1)(2) 2(−1) √ = −1±−21+8 √ −1± = −1±3 −2 −2 −(1)± x1,2 = x1,2 √ −b± b2 −4ac 2a = −1+3 −2 = = −1−3 −2 = −2 = = −1 −4 −2 =2 −2x2 + x + = a = −2, x1,2 = x1,2 = x1,2 = x1 = = c=3 √ −b± b2 −4ac 2a √ 12 −4(−2)(3) 2(−2) √ −1± 1+24 = −4 √ −1± 25 = −1±5 −4 −4 −(1)± x1,2 x2 b = 1, −1+5 −4 −1−5 −4 = = −4 −6 −4 = −1 = 4x2 − 3x + = a = 4, x1,2 b = −3, = c=1 √ −b± b2 −4ac 2a Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Full file at https://TestbankDirect.eu/ Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at https://TestbankDirect.eu/ x1,2 = x1,2 x1,2 = √ 3± −7 = x1,2 x1 x2 √ (−3)2 −4(4)(1) 2(4) √ 3± 9−16 = √ 3± 7i2 i2 √ = 3±8 7i √ = 3+8 7i √ = 3−8 7i −(−3)± = −1 −2x2 + 4x − = a = −2, b = 4, = x1,2 x1,2 = √ −b± b2 −4ac 2a x1,2 x1,2 x1,2 x1,2 x1 x2 √ 42 −4(−2)(−3) 2(−2) √ −4± 16−24 = −2·2 √ = −4±−4 −8 √ 2i = −4±2 −4 √ = 2∓2 2i √ = ± 22 i √ = + 22 i, √ = − 22 i −(4)± x1,2 c = −3 3x2 − 4x − = b2 − 4ac a = 3, b = −4, c = −7 (−4)2 − 4(3)(−7) = 16 + 84 = 100 > −1 3x2 − 4x + = b2 − 4ac a = 3, b = −4, c=7 Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Full file at https://TestbankDirect.eu/ Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at https://TestbankDirect.eu/ (−4)2 − 4(3)(7) = 16 − 12(7) = 16 − 84 = −68 < √ 2+ 17i √ 2− 17i −x2 + 2x − = b2 − 4ac a = −1, b = 2, c = −1 (2)2 − 4(−1)(−1) 4−4=0 4x2 − x + = a = 4, b = −1, c=1 b2 − 4ac (−1)2 − 4(4)(1) = − 16 = −15 < √ 1+ 15i √ 1− 15i 3x2 − 5x + = a = 3, b = −5, c=6 b2 − 4ac (−5)2 − 4(3)(6) 25 − 72 = −47 < √ 5+ 47i √ 5− 47i −x2 + 7x − = a = −1, b = 7, c = −2 Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Full file at https://TestbankDirect.eu/ Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at https://TestbankDirect.eu/ b2 − 4ac (7)2 − 4(−1)(−2) 49 − = 41 > √ 7+ 41 √ 7− 41 z = a − bi z = a + bi (z) = (a − bi) = a + bi = z z = (z) z+w =z+w z = a + bi w = c + di z + w = (a + bi) + (c + di) = (a + c) + (b + d)i = (a + c) − (b + d)i z = a + bi, w = c + di z = a − bi, w = c − di z + w = a − bi + c − di = (a + c) − (b + d)i z + w = (a + c) − (b + d)i = z + w z = a + bi w = c + di zw = z · w z · w = (a + bi)(c + di) = (ac − bd) + (ad + bc)i = (ac − bd) − (ad + bc)i Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Full file at https://TestbankDirect.eu/ .. .Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at ± (2x + 4) = ± (5x − 2) = 5x − 2x + 2x... © 2011 Pearson Education, Inc Publishing as Prentice Hall −3 Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at −6 < 2x + < −9 < 2x < 3 − 4x ≥ x≥ − 92... Copyright © 2011 Pearson Education, Inc Publishing as Prentice Hall Solution Manual for Calculus For Biology and Medicine 3rd Edition by Neuhauser Full file at −x − + 2y − 10 = −x + 2y − 13 = A = −1