For what value of k, if any, is * kxe-2a dx = 1?

Q: (b) Guess the value of dx when n is an arbitrary positive integer.

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Q: S²³² The numerical value of -3√9-2 dx will be equal to

A: Given that ∫-33x9-x2dxSolution:odd even property if f is odd f-x=- fx  then ∫-aafxdx=0

Q: d (a) dx 2 1 + x

A: Topic:- derivatives

Q: Complete the following statement. If dy/dx is small, then smallchanges in x will result in…

A:

Q: Assume dx 6 and | g(x) dx = –-3. Evaluate each of the following:

A: Given as ∫05fxdx=6 and ∫05gxdx=-3

Q: the following 2 √x² √₁ + x dx aluate

A: Given query is to find the integral.

Q: when step Qal Evaluate the x²+2Xy + y? dy dx Size of x=0,2 and step size of y= 0.5

A: We have to solve ∫01∫02(x2+2xy+y2)dydx Given step size of x = 0.2 and step size of y = 0.5

Q: 3. 4x 3 + dx

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Q: The area to the left of Z= -0.11 is?

A: The standard normal variable is z, which follows the normal distribution with the mean of 0 and…

Q: 4. Find an approximate value for fo In 1+x³| dx.

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

Q: dx Find the value of if it exists. x2 – 1 1 8.

A: I=∫1∞dxx2-1=∫1∞dxx+1x-1=12∫1∞2dxx+1x-1=12∫1∞x+1-x-1x+1x-1

Q: solve the following integoal రయి dx 22 Nx²+5

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Q: Find the antiderivative of the following: х — 5 - f(x) - 7 dx %3D

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Q: find x for which = 0. dx

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Q: 5. /2хе-2х dx

A: Given:       ∫ 2xe-2xdx

Q: If y = (In x + 1)(2x³ – 3x), then will be dx

A: Differentiate wrt x

Q: Evaluate e 2 e D dx 2 X (LAX) ²

A: In this question, we want to evaluate the given definite integral.

Q: 2. Find S x?e* dx.

A: topic - integration

Q: Find ds/dx if= y= In[(2x^3+7) (9x-2x^2)]^5 Hint: Use the Tattoo and the Properties of Logs

A: Given y=ln2x3+79x-2x25 Using properties of ln, 1) ln an=n·ln a 2) lna·b=ln a+ln b  y=5…

Q: Let ƒ(x) = x3 - 3x2 - 1, x>= 2. Find the value of dƒ -1/dx at the point x = -1 = ƒ(3).

A: We will need inverse function theorem. Statement of the theorem is:

Q: (3y³ – x³) dx = 3xy² dy; y(1) = 2

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Q: Suppose f(2) = 1, f'(2) = –6, and | dH H(x) = (1 + f(x))³. Find dx Н (2) %3

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Q: QUESTION 9 Compute the following. d x5+17x3+39x²+13] dx

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Q: d Find {In(eª + e¯#)} dx

A: Given that: ddxlnex+e-x

Q: Integrate the following: S (x4 – 5x³ + 6) dæ - 1. 6 so(1– so(1- dx

A: 1. Integrate ∫x4-5x3+6dx  Solution: ∫x4-5x3+6dx =∫ x4dx-∫ 5x3dx+∫ 6dx     sum rule=x55-5x44+6x…

Q: 2 + dx

A: Given :∫5x-3x2+2x4dx

Q: Complete the evaluation of V4 x make sure to express your answer in dx in Example 2; terms of x.

A: Consider the provided integral, ∫x24-x6dx Solve the above integral and write down the answer in term…

Q: – 1)*dx

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Q: Suppose that (x) dx=3 and g(x) dx=7, then what is 1 8. 8 the value of (х) dx ? 1

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Q: et Evaluate dx using an appropriate substitution. 1+ e2x a

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Q: S 2x(x² – 2x)dx

A: Solving the problem by finding the value of the integration.

Q: find dz e 1-e |

A: To find the given Integral.

Q: Find the value of b so that (2x – 1)dx = 10 - 1 3 O 2

A: We have to find out b

Q: How's f', and g'(x) used in composites d/dx for deriving

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Q: What are all values ofk for which x'dx = 0?

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Q: S x(x² – 1)dx

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Q: Write your answer using L (x) defined in the previous page. E (-1)" (2n + 1) / dx g² + n + 1)´ ( 27…

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Q: 2. Evaluate the following: . /32 dx a. b. /a'e'dt c. [e*se" dx

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Q: Derive a formula for the equation below: хп In x dx Where a.) n =-1 b.) n + -1

A: We use  the substitution method and integral by parts for each of the cases given. Note that…

Q: 1 dx (2x + 1)'

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Q: Solve the following D·E 5) + ycotx = 5ecosx dx

A: The given differential equation is a linear differential equation We have to find the solution for…

Q: Evaluate e (r- 2|) dx if it exists. If it does not exist, explain why.

A: To evaluate: ∫-12x-2|x|dx

Q: dt x-5

A:

Q: ..... Q.5 Show that s! dx= 2a"

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Q: C. Find Sx® In 3x dx using by Part techniques.

A: Here we will use the formula of integral by parts. Assume, f(x) = ln(3x) and g(x) = x^8 Formula will…

Q: Without using a calculator, determine d/dx{2e^3x *cosh 4x−e^7x} in simplest terms.

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Q: Prove the reduction formula S x"e*dx = x"e* – n S x"-'e*dx

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Q: Let ƒ(x) = x2 - 4x - 5, x> 2. Find the value of dƒ -1/dx at thepoint x = 0 = ƒ(5).

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Q: B D 3. d²y and -both dx? dy 1. At which of the five points on the graph in the figure above are dx…

A: Given, The graph between y and x  Fiven points A,B,C,D,E  are given on the graph