How do I show that F(x) are antidervatives of f(x)?

Q: 3. Consider f (x, y) = a +6V-10. Compute the following: (a) (b)

A: Given,          fx,y=x4+6y-10

Q: Let f(x) 11 In(x). Then f'(x) is andf (8) is f"(2) is and f(8) is

A: Use differentiation for finding the values

Q: If z = f(x) + yg(x), what can you say about zy? Explain!

A: Answer is 0

Q: 7. f(x)= // at x = [0, 1]

A: Given: fx=1ex3 ,x=[0, 1] To find: n when error E=0.0002. To find: Approximate integral by using…

Q: 1. f (x² + 1)(x² + 3x) dx

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

Q: An antiderivative of f(x) = 5x4/3 + + 2x5/4 is %3D

A: The given function is fx=5x43+2x54. The antiderivative of ∫xndx=xn+1n+1+C.

Q: Find f(") (x) given f (x) = In(x + 1)

A: Given function is  f(x) = ln(x+1)  We have to find the nth derivative of f i.e. fn. We use  notation…

Q: Let f(x) = V9 – x², 0sxs 3. (a) Find f-1. f-1x) = (for 0 s x < 3) How is it related to f? O t is the…

A: Given Data: Function: fx=9-x2 Interval: 0≤x≤3 The inverse function can be obtained by substituting…

Q: 7 x + 2 Let f(x) = x4 . x + 5 f'(x) = %3D

A:

Q: 2. Determine the area under the curve y = on [0, 1].

A:

Q: 8. If f(x) dx = f(x) + C, determine f(x). Justify your answer. %3D

A: Given, ∫f(x)dx=f(x)+C Differentiate both sides with respect to x, we get f(x)=dfdx…

Q: On a test, a student makes this statement: "The functi f(x) = x² has a unique antiderivative." Is…

A:

Q: Use the linut definition to Compute f(x) when f)-at. the derivative f(x) when f)-2+L

A:

Q: Let f'(x) = x*+4x³ + 2x² + 12x+1. a. For what values of x is f(x) concave up? (Blank 1) b. For what…

A: The given first derivative function is

Q: f(x) = ex/³; [1₁3]

A:

Q: Suppose f(x) and g(x) are two functions such that: • f(3)=1 • g(3)=1 • f(3)=5 • g'(3)=7 What is…

A: we know that uv' = u'v+v'u                   product chain rule of differentiation

Q: The inverse of function f(x) = x3 + 2 is а) f-1 (y) %3 (у - 2) 1/2 b) f-1 (y) = (y – 2) 1/3 c) f-1…

A:

Q: If f(x)=xcos x , then f'(E) equals +1 (e) 1-2 (b) (a) 2 (d) (e) none of these - 2

A: Given  f(x) =x  cosx Find: f'π2 Solution: Formula: ddx(uv) =udvdx+vdudx       ---------------(1) Let…

Q: 22. Find f/(x) and simplify 1 -1 a) f(z) 3-52+1 3 b) f(x) 1.8Vc) f(x) = 32

A: Given, functions

Q: Find the following using the table below. 3 4 f(r) f (x) g(x) 4 4 4 3 4 (x),6 h'(2) if h(x) f(x) ·…

A: It is given that h(x)=f(x)⋅ g(x), h(x)=f(x)g(x), h(x)=f(g(x)) We have to find h'(2).

Q: 1(b)   Answer with "true or false". In addition, if the answer is wrong, correct the statement.…

A:

Q: Let f(z) z+ 12 f'(2) =

A: Given that: f(x)=1x+12

Q: If f(x) = 1 – then f (F(F(x))) = then f (f(f(x))) = |

A:

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

A: The function given to us is as follows: fx=x+1x2+1 at  x=0, 3 We are asked to find the integral of…

Q: Fermat’s Theorem does not claim that if f'(c) = 0, then f (c) is a local extreme value (this is…

A: The given statement is “Fermat’s Theorem does not claim that if f'(c) = 0, then f (c) is a local…

Q: 3. If L{F(t)}=f(p) then L{F(at)}= (a) f(2) (b) 음/ (B) (c) af) (d) 금f(ap)

A:

Q: Let F(x) be an antiderivative of f(x), with F(1) = 20 and * f (x)dx = -7. What is F(4)?

A: