-5 #2. Suppose that S„ƒ(x)dx= 6 andS²,g(x)dx= -4. Find S°,[3f(x) – 0.5g(x)]dx.

Q: 1. Find the instantaneous rate of change when x=π for y=sin*x/2-3cosx.   2. Interpret geometrically…

A: Simply take the derivative and put the given point to find the instantaneous rate of change.

Q: '5 f(x) = -9 evaluate the following. J2 2 Given f(x) dx = 3 and (a) f(x) dx (b) f(x) dx '3 (c) f(x)…

A: Given : ∫02fxdx = 3 and ∫25fxdx = -9   To find : (a)∫05fxdx (b)∫52fxdx (c)∫33fxdx (d)∫25-8fxdx

Q: SO f'(2x) dx. +6 Lºx xf"(x) dx.

A: The given integral expression is:∫04 f'(2x) dx

Q: Suppose that f(x) = √3+e. Find ƒ' (2). f'(2) =

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Q: For the function f(x) = 7x – 3x+ 4, find f'"(x). Then find f"(0) and f''(6). f"(x) =(Simplify your…

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Q: x² d. Find dx (e" -tant)dt. tan(x?) a. 2x(e** - tan(x?)) Ob. 2xex - sec?x O c. O d. It is impossible…

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Q: For the function f(x) = find f'"(x). Then find f''(0) and f'"(4). %3D 2+x f"(x) =] Select the…

A: We will differentiate f twice and then evaluate at x = 0 and at x = 4

Q: Find the second derivative of the function F(t) Answer = 4tsin (14). F"(t) =

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Q: 37/2 rcos(x) dx where f (x) =xcos(x) is graphed to the right. 10. Find f(x)

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Q: 1 3. Let f (x) = 4x +- х Find f'(x) S f(x)dx а. b. Find

A: Here given as fx=4x+1x Differentiate as f'x=ddx4x+1x=ddx4x+ddxx-1=4-x-2=4-1x2

Q: For each problem, find the function f based on the information given. 13. f'(x)=√x(6+5x) 14.…

A: 13) Given:  f'(x) = x6+5x ⇒f'(x) = 6x12+5x32 Integrate both sides with respect to x we get

Q: What is the process for finding dy/dx when y is an implicit function of x? Illustrate with an…

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Q: 12. Find the derivative of the following function. y = 71n(x -4) a. x3-4 b. Зx? х* c. d. 21x?

A: To find the derivative of the below function.          y = 7ln[x3 – 4]