Use an appropriate substitution to prove f(x)dr f(a + b – x)dr.

Q: he Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 5+x2 Ciuo Hooim

A: Here we have to use linear approximation rule.

Q: Integrate f(x) from x = 2 to 8 using Three-Point Gauss-Legendre Quadrature. f(x) = 5000+24563x -…

A: Gauss legendre quadrature gives the result of integration over a symmetrical limit of variavle x…

Q: Find the antiderivative F of f(x)=4-3(1+x^2)^-1 that satisfies F(1)=-2.

A:

Q: Find the funchion f Such that F(x) xf (x)-x and fo) 2

A: Convert the given problem to a simple differential equation and solve the same.

Q: ): Apply Rolle's theorem for the function f(x) = 9x² – 36x + 27 over the interval [1, 3]. Justify…

A: Given :- Apply Rolle's Theorem for the function fx = 9x2 -36x + 27 over the integral 1,3.

Q: Evaluate f''(c) at the point. f(x) = (x2 - 4)(x3- 2), c = 1

A:

Q: Differentiate f(x) = a4x4 -3ax² with respect to x. Assume that a is a constant. f'(x) =

A: f(x)=ax4-3ax2 differentiate with respect to x

Q: Does the MVT apply to f(x) =- x²_3x+5 on the interval [-1, 2]? (x-1)

A:

Q: Consider the function f(x)=5x+6x^2 over the interval [0,1].

A: Given that :-         f(x) = 5x+6x2 over [0,1] (a)  By deviding the interval into n sub intervals of…

Q: Let f(x) = +.Compute the difference quotient for f(x) at x = 4 with h = 0.3 %3D difference quotient…

A: Given,

Q: Prove that for all a, b = R, the function f(x) = 3x² - 4x³ + 6x² + ax + b has exactly one point…

A:

Q: if f(x) is a function that is continous at (2,f(x)) then f(x) is differentiable at (2,F(2))   true…

A: Given statement is If f(x) is a function that is continous at (2,f(x)) then f(x) is differentiable…

Q: Explain why

A:

Q: Find f(x) iff, (p) Hence deduce F .

A:

Q: For f(x) = sinx, compute f ' at x = 0, π/6 , π/2 , 5π/6

A: Given, fx=sin x

Q: 2. If f(x) = 1 + x², find fof 3.lf f(x) = -x, g(x) = 2x + 1 and h(x) = x², find fogoh,

A:

Q: 6. Use an appropriate substitution to prove f(x)dr = | f(a+b- x)dx.

A: To use an appropriate substitute to prove  ∫abfxdx=∫abfa+b-xdx

Q: If you need to prove that a ∈ f^−1 (Y ), what do you need to show?

A: Here we need to show the way to prove a∈f-1(Y)

Q: If f(x) is continous on [a,b] then f(x) is differnitable on (a,b). True or False?

A: False Any differentiable function must be continuous at every point in its domain. The converse does…

Q: Let f(x) = 4x^2 – 7x. Use the ɛ/8-definition of the derivative to prove that f'(2) = 9.

A:

Q: a. Differentiate f (x) = x²lnx with respect to x b. Proof that f" (2x + 4xlnx)dx = 2e2

A:

Q: Determine whether f is continuous or not at x = 2. Justify your answer and state your conclusion.…

A:

Q: Integrate f(x) from x = 0 to 10 using Three-Point Gauss-Legendre Quadrature. f(x) = 5000+24563x -…

A: Given f(x)=5000+24563x-7418x2+768x3-31x4+0.14x5 Let I=∫010f(x)dx Here a=0 and b=10

Q: Use the Second Fundamental Theorem of Calculus to find F′(x).

A: To find the derivative using fundamental theorem of calculus.

Q: Let f(x) = 3x In f'(x) = 3x1 + 15x1 In(a) f'(e?)

A: We have to solve

Q: Find the best quadratic approximation to f on the interval [ -1, 1].                     f(x) = lxl

A:

Q: Proceed as in Exercise 51 to calculate F'(0), where 3x + 5x* + 5x +1 F(x) = (1+x +x*/3 +x/³) : 8x9 –…

A: Given function is Fx=1+x+x43+x533x5+5x4+5x+18x9-7x4+1. First multiply the numerator.…

Q: 2. If f"(x) = 4sinx+16cosx, f(0) = 6, f'(0) = 1, find f(x) and f(4).

A:

Q: What is f' (x) when f(x) = 5e%z?

A: The given function fx=5e4x Differentiate with respect to x using the chain rule f'(x)=5de4xd4x×d4xdx…

Q: If f(x) = cosh-'(5x), then f'(x) %3D

A:

Q: Prove that f (x) = x2 takes on the value 0.5 in the interval [0, 1].

A: Here given

Q: Find a function f(x), such that f"(x) = 3sin(4x). %3D

A:

Q: - Given f(x)= -, find f(x). 2+x %3D 6.

A:

Q: Use the intermediate value theorem to show that f(x) = e-x2− x has at least one root in the interval…

A:

Q: Use the Intermediate Value Theorem to show 11. f(x)=2x' +3x-1 has a zero between a = 0 and b = 1.

A:

Q: What is f'(3) if f(z) = z/2z - 2 I.

A: d(xn)dx=n(x)n-1

Q: Given that f(x) = 4x2 − x + 2, use the limit definition of the derivative to compute f'(x).

A:

Q: Find f'(x) for f(x) = In(x* + x²) with x # 0. %3D

A: Given, f(x)=lnx4+x2, x≠0

Q: What is f'(x) at x = -1 of the function f(x)=x^-2 + (x^2)^(1/2) *

A:

Q: Can you apply Rolle's Theorem to f(x) = x3?

A: Given that f(x) = x^3 Since f(x) is strictly increasing continuous function , therefore     (1).…

Q: Use this definition to find f'(a) at the given number a. f(x) = V6x + 7,

A:

Q: Find the interval(s) on which f(x) = 2x^3-3x^2-12x+1 is concave up.

A: Given : fx = 2x3 - 3x2 - 12x + 1

Q: , for x 1 Let f(x) be a function defined by f(x)=- Discuss the contuniuty of f and f'.

A:

Q: Verify Rolle's theorem for f(x) = x² - 9x +6 over the interval [0, 3].

A:

Q: ) Use the Intermediate Value Theorem to show that there is one such that f"(a) = 0. point x = a

A: As per our guidelines we are supposed to answer only first 3 subparts of the question. Kindly repost…

Q: If f(x)=x', find f'(x), f"(x), f'''(x). (Pls 2. use the definition method)

A:

Q: 2 Determine f(x), given f'(x) = x´ – 3x + 1, and f(0) = 2.

A: As per the company guidelines we are supposed to answer only the first question.Kindly repost the…