5 Given that f f(x) dx = 13, evaluate the following integrals: (a) f3 f(r) dr = 3 (b) f f(x) dx (c) f., 7 dx (d) fs (10 f(x) - 7) dx = =

Q: Consider the function Compute f"(x). X = 66²⁰ - f(x) = -3t²- f"(x) = -4t+ 3 dt.

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Q: 2. Find f'(1) if f(x) = 3x³ (√x-2).

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Q: Suppose v(t) gives a particle's velocity at time t , in miles per hour. Write an integral expression…

A: Let the particle velocity v(t) at time t , (in miles per hour)

Q: 8 6. * f(x) = 7 + + find f'(x). - x2 Find f'(2). | 8

A: To find the derivative we use power rule of derivative formula. Power rule of derivative is…

Q: Find f    if  f'(x) = 7x9 − 5 √x + 3 sin x,   f(0) = 4

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Q: Let f(x) = x^2 + 15  ^5√ x and g(x) = 3 − 2x. Find the following: d/dx(x^2g(x))

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Q: Show that cosh (3x) = 4cosh³r - 3 cosh T.

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Q: Integrate (2x - 5) with respect to x from x = 2 to x = 5.

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Q: Let f(x)=100/5+2e-0.01x. Find f'(x).

A: Write the given function using exponent.

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Q: B. Using Change of Variables and Generalized Power Formula, integrate the following: 1. fx (x2 –…

A: Since we have multiple numbers of question and our guideline is solve first question and kindly…

Q: nd frr for the function z = x ° - 6xy+ 4y .2 30x 2- 42x 6x- 6y

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Q: Differentiate the following function. 6x2 +5 y = x2 +1 dx (x² + 1)< dy (x² + 1) • : (6x² + 5) + (6x²…

A: You just need to apply quotient formula in order to solve this.

Q: If a = 1 − v^2 and both x and v are zero when t = 0, show that x = −1/2ln(1-v^2) and hence find v^2…

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Q: 10 dx (х3-10х+5)1/3 -2

A: Given integral is ∫−2010x3−10x+513dx We have to evaluate ∫−2010x3−10x+513dx by trapezoidal rule. The…

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Q: . Evaluate S (-+ 3e* ) dx

A: We have to Evaluate  ∫ {(1/√x) - (2/x) + 3ex} dx = ∫(1/√x) dx - 2 ∫(1/x) dx + 3 ∫ex dx

Q: Evaluate: 2 (1) (2-3)* dx 1 1 dx x + 5 (2)

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Q: Evaluate 1 dx (x - 2)³

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Q: Integrate the following: 1. fxsinxdx 2. fæcos2xdx 3. fe sinxdx

A: The given integrals are' 1) xsinx 2)xcos2x 3)exsinx.  Repost the next parts.

Q: Differentiate f(x) = Vx² + 1(³. Do not simplify. x+2"

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