By the even extension method applied to the function f (x) = e¬19x, where x > 0, the value of the integral 00 cos(8w) dw = 361 + w2 1. el52 19 1 2. es 38 3. e-152 38 4. л е-8 e-19 38 Select one: 1 2 0 5 4. 5.

Q: Find f'(x) for f(x) = - 8A√x - 5Bx⁹ where A and B are constants. Completely simplify any fractions.…

A: Solution of given question is written in below steps.

Q: Suppose that f(x + h) – f(x) = 5hx + 8h – 6h². Find f'(x). f'(x) =

A: Given: fx+h-fx=5hx+8h-6h2, To find: f'x.

Q: The function f(x) = 3x³ + cos(3ræ) + 2x , x > 1 is known to be a strictly increasing function on its…

A: Given f(x) = 3x3 + cos(3πx) + 2x,  x≥1   ⇒ f'(x) = 9x2 - 3πsin(3πx) + 2

Q: 4. Find (f-1)'(1) if f(x)=x' +8x+sin(3.x) а. Find (f-1)'(2) if f(x)= Vx' +x +xr+1 b.

A: To find the derivative of the inverse of a function

Q: Given that f(u) = ln7 + 4u - 15e9 - 7u-3. Determine the value of f''(0). a. Negative Infinity b.…

A: Given function is , f(u)=ln7+4u-15e9-7u-3 differentiating with respect to u, f'(u)=4+21u-4…

Q: 1. Find the equation of the lines tangent and normal to the curve 3x?y2=4x2-4xy. at the point…

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: Find the third derivative of f(x) = 3√x³-5cosx. 45 O f(x)= 4553 9 O f(x)= - O f(x)= 45 O f(x)= - 9…

A: It can be written as f(x)=3x3/4-5Cos(x)

Q: Your used Chevy’s gas mileage (in miles per gallon) is given as a function M(s) of speed s in miles…

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Q: 2 For the function f(x)=√x+25, find f''(x). Then find f''(0) and f''(3). f(x)=0 www

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Q: O X 3. Find f'(x) when f(x) = √16x²

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Q: If f'(2) = 5 then [4f(x) – x³]x=2 %3D dx Select one: O 32 O 8 O 28 O 20 O none

A: Given f'(2)=5To find ddx[4fx-x3]x=2

Q: IV. Exercises A. Solve the following integrals: (1) /20. (2) / (2e + 4"). da (3) 2(5") dr

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Q: If f(2x) = 5x2 + 3, then f'(2) = %3D О а. 5 O b. 6 О с. 2 O d. 10 O e. 3

A: Given ,  f(2x) = 5x2 + 3 then  We have to find the value of f'(2)

Q: Let ø be a C' function, and suppose 00 $(x) = >, b,Un(x)., ø"(x) = ), cnUn(x). %3D n=1 =1 Express…

A: Here in the question it is give that ϕ is a C1 function .  Consider the given function as follow:…

Q: Goal: Find the integral 18x cos(6x)da using integration by parts via the tabular (DI) method. First,…

A: We know that: ddxxn=nxn-1∫cosax=1asinax∫sinax=-1acosax

Q: (a) Using integration by parts, find fx sin(2x - 1) dx. (b) Use substitution method to find x² 2x-1…

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Q: Suppose F'(x) = 5x² + 6 and F (0) = 1. Find the value of F (b) for b = 0, 0.1, 0.4, 0.8, and 2.0.…

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Q: v 1. y = x³/2 ? v 2. y = 2/(x³) v 3. у 3D 14x12 ? v 4. y = 3x' + 2x? 5. у 3D 12. 14* ? 6. y = V4x4

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Q: Determine the value(s) of æ for which f' (x) > 0 given that f(x) = (-4x² + 25)² 5 00, b) О .o() ()…

A: Solve the function

Q: If f(x) = 5x, then f'(2) = %3D %3D O 15x? O 40 O 30 O 60

A: We want to find the value of the derivative of the given function at x=2. The given function is…