Suppose f(x) has the following properties: f(3) = 8 f(9) 6 [ f(x) dr z f(x) dx = 13 [₁ 2² f(x) dx = 10 Evaluate: 10 [(5x² + 6x + 5) f'(z) dx =

Q: Consider the function f (x) = 6x² + 4x + 2. Find F(x) so that F' (x) = f(x). %3|

A: f(x)=6x2+4x+2To find: F(x) such that F'(x)=f(x)

Q: 1. Find the general form of f if f'(x) = 4(x).

A: We have to find the general form of the function f if f'x=4 fx. Rewriting the given equation, f'x=4…

Q: (2-9x³), find f'(x). Given f(x)= In (2-9x³), f'(x) =

A:

Q: Suppose f(x) √₂+² = √1+tdt 2x find f'(1).

A:

Q: Let S(x) = 4x$ (x' – 6). Evaluate the following specific values of f: (A)(2) = (B) (4) =

A: The objective of the question is evaluate the values.

Q: 1. f (x² + 1)(x² + 3x) dx

A: To evaluate the given integral.∫x2+1x3+3x4dx

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: Suppose F(5) = -7, F(9) = 3, and F'(x) = f(x). = [ 7f(x) dx

A:

Q: Find the derivative of the following functions a) f(x) = 1 + x² + = 160 1x x6 I b) F(X) x4-3x+1 √x…

A:

Q: Find f" (1) when f(x) = x² − 3x³ + 2x² +10. Round your answer to three decimal places, if necessary.

A:

Q: Find the approximate integral of the following function using Simpson's 3/8 rule and determine the…

A: Given: fx=ex2, x=0, 4, E=0.0002 To find: n To find: Approximate integral.

Q: . If f(x) = V4x – 7, find f'(x).

A: we have ;  f(x)=4x-7;  we have to find f-1(x)

Q: 17 [," Farde - [." Farde - [." Her de f(x) dx f(x) dx = = f(x) dx

A: given that  ∫317f(x)dx-∫311f(x)dx = ∫abf(x) dxthen we have to find value of  a and b   since we know…

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: f(x) = 3x² (1 + 7x-3

A: The given function is:fx=3x21+7x-3

Q: (2 11) dx (x+2)* (x-1) *

A:

Q: 8. Find f'(x) for (a) f(x)=(x² +3x+1)(2x+3) 2x-3x+1 (b) ƒ(x)= %3D

A: We need to find the derivative of the given functions. For (a),

Q: f(3) f(9) f(x) dx 3 9 [² x f(² 9 x f(x) dx x² f(x) dx Evaluate: = = = 8 6 16 18 = 13 9 ( − 8x + 6)…

A:

Q: If f(x) = 6 + 5x – 5a, find f'(- 3).

A: Topic = Derivative

Q: Use the second derivative to determine f"(4) for the function f (æ) = x² In (x) 2ln(4) +2 3ln(4) +3…

A: Derivative of the function

Q: 7) Find √ (1/1₂ + 3x + 2) dx

A: Given problem:- ∫4x2+3x+2dx

Q: Suppose f(z) has the following properties: f(6) = 3 f(10) = 8 10 f(z) dz = 12 10 [" I f(z) dr = 10…

A:

Q: 2. Determine the exact value of f'(2) for f(x) = (2e³ + 3e-6x)5.4,

A:

Q: If f(x) = x' – 8x + 2, find f (-4).

A: We have,  fx=x3-8x+2           ⋯⋯1

Q: Find f. f(x) = f"(x) = -2 + 18x - 12x², f(0) = 3, f'(0) = 12

A: Integration

Q: 9. [f(x)dx -1

A: Find the integral from the given graph

Q: Given f(x) = x + 4, x < 0. Find (f-1)' (5) 10 1 2 | 29

A:

Q: 15 .3 Suppose f(x) da = 2. f(x) da | f(x) da = 5. What is | f(æ) da? 3, and -8 -10 10

A:

Q: Compute f(x)dx f(x) = { 2x if x <1 4 if x 21

A:

Q: 4. x(x² – 1)² dx

A: Solution:

Q: Suppose that f(x + h) – f(x) = 7hx? – 8hx + 5h²x – 3h? – 7h³. Find f'(x).

A: The quotient difference formula is given as, f'x=limh→0fx+h-fxh it is given that…

Q: 2. What is the second derivative of f(x) = - ²x³²x²+6? f"(x) = 5x² - ²³√x f"(x) = 10x + √√√x+6 a. b.…

A:

Q: If f(x)- Vu² - 1 du, then what is f'(3)?

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Sketch the following functions. Show all your work. N a) Domain b) Intercepts c) Symmetry d)…

A:

Q: 10. f(3x - 1)(x - 1) dx

A: The given integral is:∫-113x-1x-1dx