|f[*„ƒ(x) dx = 1. [*²ƒ(x) dx - = 2. [*19(x) + 2] dx = = -5, 5. [ƒ(2) dx = 12, and [9(2) dz = 8, find the following integrals.

Q: ƒ' (4) = If f(x) = 3√√√x(x³ − 2√x + 2), find f'(4).

A: Given that

Q: 1 4 √x 5 18 dx =

A:

Q: /25 – x² (-2x) dx 11.

A: 11. According to question,Given integral,∫25-x2-2x dx

Q: Find f. f"(x) = −4+ 8x - 12x², f(0) = 4, f'(0) = 12 (Prob. 1,

A: Consider the derivative function and initial conditions, f''x=-4+8x-12x2,f0=4,f'0=12 The objective…

Q: find the diferential of the function when x = 2 and dx = 0.1 f(x) = x ln (x^3 + 2x - 4)

A: We will use the definition of differential.

Q: Find the indicated derivative or integral a. D, (3** * ) c. D, log,, (x³ +9) –3x а. D, b. |x 2* dx…

A: We know that Dx ax = ax·ln(a) Dx af(x) = af(x)·ln(a)·f'(x)   ∫ax dx = axln(a)+C   Dx loga x =…

Q: Please help me. *If y = √u+1 and U = 5x+1, then dy/dx is

A:

Q: Find an expression for h'(x).  h(x) = 2 f (2x + 1)

A: Given equation - hx = 2f2x+1    .........(1)

Q: Find all possible functions with the given derivative. y' = 2x² - 6x 2 O A. 3x³ + C 2 O B. 3x³-3x² +…

A: Given,             y' = 2x2 - 6x

Q: dy + ydx = 3x²y?dx, %3D

A:

Q: / x(8x + 9)" dx %3D

A: Using Liate's rule for integration we can solve the above problem. This is also known as the…

Q: Find the second derivative (y") of the given function: 6. y 2-e -6e* +12e-e" (2-e*)" 6e* (2+e*)…

A:

Q: Find f. f"(x) = -2 + 36x - 12x2, f(0) = 2, f'(0) = 18

A: Given, .Given,  f(0)=2, f'(0)=18.We know,

Q: Find f. 3 f'(x) = 1 - x? f(x) =

A:

Q: For each of the following y, find the d^2y/dx^2

A: We know, d/dx (xn)= nxn-1, for any real number n. d/dx(u(x)v(x))= v(x)*d/dx(u(x))+u(x)*d/dx(v(x))

Q: r(x) = 3x/4- x0.1/3 + 5/4x1.1 - 3 r'(x) =

A:

Q: derivative

A:

Q: If f(x)= ∫ (top 16, bottom 9) (-x^(-1/2)+5) dx. Enter your answer as an exact fraction of necessary.

A:

Q: Determine the particular solution of the ODE y” + lnx = -1 a. (-0.5 * lnx) + 0.25x b. (0.5x^2 * lnx)…

A:

Q: A company finds that the revenue R generated by spending x dollars on advertising is given by R =…

A: To find: The value of dRdx at x=1500. Given: The revenue generated function is R=1000+80x-0.02x2.…

Q: For y=f(x)=3x^3 , x=3 , and (triangle)x = 0.03 find dy (two decimal places)

A:

Q: Find -2 (2x5+ 3x¹) dx

A: Given that a integration and we solve this integration by using general property of integral.

Q: Vx² + 100 -10 lim x²

A: We are solving the first question and for the next question post the question again and also mention…

Q: find d/dx f^-1 (4) where f(x)=4+2x^3+sin((pi*x)/2) for -1

A: We have,.We have to find .

Q: Find d/dx((x)(d/dx(x-x^2))

A:

Q: х — х* - 3х - 2 X | dx x* - x'+ 4x – 4x 3

A:

Q: f'(x) 6 48 3 8 Write down the value(s) of x for which the original function y = f(x) is a.…

A:

Q: 1. x'-11/x +2 dx

A: