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Solution Manual for Thomas' Calculus, SI Units, 15th edition Joel R. Hass Christopher E. Heil Maurice D. Weir £12.68
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Solution Manual for Thomas' Calculus, SI Units, 15th edition Joel R. Hass Christopher E. Heil Maurice D. Weir
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Solution Manual for Thomas' Calculus, SI Units, 15th edition Joel R. Hass Christopher E. Heil Maurice D. Weir

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  • September 18, 2024
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Solution Manual for Thomas'
Calculus, SI Units, 15th edition




1. Limits

Question: Evaluate the limit of lim⁡x→3x2−9x−3\lim_{x \to 3} \frac{x^2 - 9}{x -
3}limx→3x−3x2−9.

A) 3
B) 6
C) 9
D) 0

,Answer: B) 6

2. Derivatives

Question: Find the derivative of f(x)=5x3−2x2+4f(x) = 5x^3 - 2x^2 +
4f(x)=5x3−2x2+4.

A) 15x2−4x15x^2 - 4x15x2−4x
B) 15x2−2x15x^2 - 2x15x2−2x
C) 10x2−4x10x^2 - 4x10x2−4x
D) 15x3−4x15x^3 - 4x15x3−4x

Answer: A) 15x2−4x15x^2 - 4x15x2−4x

3. Integrals

Question: Compute the integral ∫(3x2−4x+1) dx\int (3x^2 - 4x + 1) \,
dx∫(3x2−4x+1)dx.

A) x3−2x2+x+Cx^3 - 2x^2 + x + Cx3−2x2+x+C
B) x3−2x2+x2+Cx^3 - 2x^2 + \frac{x}{2} + Cx3−2x2+2x+C
C) x3−2x2+xx^3 - 2x^2 + xx3−2x2+x
D) x3−2x2+12x+Cx^3 - 2x^2 + \frac{1}{2}x + Cx3−2x2+21x+C

Answer: A) x3−2x2+x+Cx^3 - 2x^2 + x + Cx3−2x2+x+C

4. Series

Question: Determine the sum of the infinite geometric series with the first term a=2a
= 2a=2 and common ratio r=13r = \frac{1}{3}r=31.

A) 65\frac{6}{5}56
B) 32\frac{3}{2}23
C) 23\frac{2}{3}32
D) 35\frac{3}{5}53

Answer: B) 32\frac{3}{2}23

,5. Partial Fractions

Question: Decompose the fraction 3x+5x2−x−6\frac{3x + 5}{x^2 - x -
6}x2−x−63x+5 into partial fractions.

A) Ax−3+Bx+2\frac{A}{x - 3} + \frac{B}{x + 2}x−3A+x+2B
B) Ax−2+Bx+3\frac{A}{x - 2} + \frac{B}{x + 3}x−2A+x+3B
C) Ax−2+Bx−3\frac{A}{x - 2} + \frac{B}{x - 3}x−2A+x−3B
D) Ax+2+Bx−3\frac{A}{x + 2} + \frac{B}{x - 3}x+2A+x−3B

Answer: D) Ax+2+Bx−3\frac{A}{x + 2} + \frac{B}{x - 3}x+2A+x−3B where
A=1A = 1A=1 and B=2B = 2B=2




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6. Chain Rule

Question: Find the derivative of g(x)=sin⁡(2x2+3x)g(x) = \sin(2x^2 +
3x)g(x)=sin(2x2+3x).

A) 2xcos⁡(2x2+3x)+3cos⁡(2x2+3x)2x \cos(2x^2 + 3x) + 3 \cos(2x^2 +
3x)2xcos(2x2+3x)+3cos(2x2+3x)
B) 2xcos⁡(2x2+3x)+6xcos⁡(2x2+3x)2x \cos(2x^2 + 3x) + 6x \cos(2x^2 +
3x)2xcos(2x2+3x)+6xcos(2x2+3x)
C) 2xcos⁡(2x2+3x)+3sin⁡(2x2+3x)2x \cos(2x^2 + 3x) + 3 \sin(2x^2 +
3x)2xcos(2x2+3x)+3sin(2x2+3x)
D) 2xcos⁡(2x2+3x)+3sin⁡(2x2+3x)2x \cos(2x^2 + 3x) + 3 \sin(2x^2 +
3x)2xcos(2x2+3x)+3sin(2x2+3x)

, Answer: D) 2xcos⁡(2x2+3x)+3cos⁡(2x2+3x)2x \cos(2x^2 + 3x) + 3 \cos(2x^2 +
3x)2xcos(2x2+3x)+3cos(2x2+3x)

7. Fundamental Theorem of Calculus

Question: If F(x)=∫0x2(t2−1) dtF(x) = \int_{0}^{x^2} (t^2 - 1) \, dtF(x)=∫0x2(t2−1)dt,
find F′(x)F'(x)F′(x).

A) 2x(x2−1)2x(x^2 - 1)2x(x2−1)
B) 2x(x2−1)−2x2x(x^2 - 1) - 2x2x(x2−1)−2x
C) 2x(x2−1)+2x2x(x^2 - 1) + 2x2x(x2−1)+2x
D) x(x2−1)x(x^2 - 1)x(x2−1)

Answer: A) 2x(x2−1)2x(x^2 - 1)2x(x2−1)

8. Implicit Differentiation

Question: Differentiate implicitly the equation x2+y2=25x^2 + y^2 = 25x2+y2=25
with respect to xxx to find dydx\frac{dy}{dx}dxdy.

A) dydx=−xy\frac{dy}{dx} = -\frac{x}{y}dxdy=−yx
B) dydx=xy\frac{dy}{dx} = \frac{x}{y}dxdy=yx
C) dydx=yx\frac{dy}{dx} = \frac{y}{x}dxdy=xy
D) dydx=−yx\frac{dy}{dx} = -\frac{y}{x}dxdy=−xy

Answer: A) dydx=−xy\frac{dy}{dx} = -\frac{x}{y}dxdy=−yx

9. Taylor Series

Question: Find the Taylor series expansion of f(x)=exf(x) = e^xf(x)=ex around x=0x
= 0x=0.

A) 1+x+x22!+x33!+⋯1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots1+x+2!x2+3!
x3+⋯
B) 1+x+x21!+x32!+⋯1 + x + \frac{x^2}{1!} + \frac{x^3}{2!} + \cdots1+x+1!x2+2!
x3+⋯

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