2. Let dx be given . If u = e* + 1, then the resulting integral is f(u) du. Compute f(3).

Q: Use l'Hospital's rule to find the limit. HINT [See Example 4.] x + 3 lim ex

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Q: Evaluate csc?x cot(cot x) dx. O- csc?(cot x) + C O cot(csc? x) + c O -In |sin(cot x)| +c O In sin(co...

A: Given query is to find indicated integral.

Q: 6. Find the derivatives of the following functions/curves: a) sin(y?) + cos(x²) = xy 1 — 2х | b) f(г...

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Q: What values of x make 3(x – 5)(x – 12)(x + 5) = 0? If there is more than one answer, enter your answ...

A: Topic = Algebra

Q: sec (In x) + sec2(In x) tan(In x) dx Given: 2x Find: du

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Q: Assume that sin(z) equals its Maclaurin series for all x. Use the Maclaurin series for sin(72) to ev...

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Q: a. The graph of a monomial function f is shown below. 25 20 15 10- 5 -5 -4 -3 -5 -10 -15 -20 -25 Com...

A: Please see the below picture for detailed solution. 

Q: Find the equation of circle and the equation of line from the following graph (3. -4)

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Q: How many ways are there to represent a function? Find the domain of the following function x²+3x+1 V...

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Q: 15-16 Find the number e that satisfies the conclusion of the Mean Value Theorem on the given interva...

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Q: Find the laylar polynomials of orders = 0,1,2,3, and 4 about x = No, and then find the nth laylor po...

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Q: 19-22 Use a triple integral to find the volume of the given solid 22. The solid enclosed by the cyli...

A: Given cylinder is x2+z2=4 and the plane is y=-1 and y+z=4 So,  y→-1 to 4-z z→-4-x2 to 4-x2 And x→-2 ...

Q: Evaluate the integral dx S 2xx - 3x2

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Q: Find the length of the curve y=z from z 0 to z=4.

A: The length of the curve is given by:  

Q: . Find the equation of the line tangent to the function at the given value of x. . Use a graphing ut...

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Q: Suppose f(x) (x + 5)(x + 2)(x + 1) a. Determine the roots of the function f. Preview b. What is the ...

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Q: A woman attached to a bungee cord jumps from a bridge that is 36 m above a river. Her height in mete...

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Q: Use sigma notation to write the Maclaurin’s series for the function  f(x)=xcosx. Show complete solut...

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Q: 2. Without specifically finding its roots, show that f(x) = 0 for some x E [1, 2] where x2 4 f(x) = ...

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Q: 3-1 4. The value of the indeterminate form from lim is 1 4r2 - I- 3 (a) 0 (b) 00 (c) 1 (d)

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Q: 5. Find the limits: a) limg→0 4 – Vx + 16 Vz – 3 b) limz→9 z - 9 t +2 c) lim→-2 |t+2|

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Q: 4. If f is a differentiable function of x and y with w = f(x, y), x = r cos 0 and y = r sin 0, show ...

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Q: dx Sz Given: 2x - 3xlnx Find: du 3 dx dx dx X dx

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Q: Given: 5e-x-6e-3x Find: u 5e-x - 6e-3x O 5e2x – 6 5e¬x-6e-3x O 5- 6e-2x

A: topic - indefinite integral

Q: 20. Given: S 10 -dx Find: formula

A: Here we have to integrate the given function.

Q: dx Evaluate xV x2 - 4 TT 2 4 O O

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Q: Vx-3-V9-x 3. lim X-6

A: Solving the problem by finding the limit of th3 function.

Q: The volume, V, of a sphere in terms of its radius, r, is given by V (r) = Tr³. Express r as a functi...

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Q: Use sigma notation to write the Maclaurin series for the function. 7sin zx 7(– 1)*,2* (2k)! (2k + 1)...

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Q: Solve the differential equation with appropriate method. Final answer should be free of logarithms a...

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Q: Evaluate the iterated integral by converting to polar coordinates. V2x – x2 5/x2 + y² dy dx

A: Explained below 

Q: Consider , xe¬**dx. What will be the appropriate solution and answer to this improper integral? A. l...

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Q: 3 y = log ( cos DIFFERENTIATE THE GIVEN:

A: The detailed solution is given below Thank you 

Q: SV + 2) /2 – 3y dy -

A: The detailed solution is given below Thank you 

Q: Find the derivative of the function f(x)=2x−73x−2 at x=2

A: topic - derivative of a function

Q: ex Given: 5e-x- 6e-3x Find: u 5e-x- 6e-3x 5-6е-2х 5e-X - 6e-3x 5e2x – 6

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Q: Csc X Given: dx Vcor?(글씨)-4cor(글씨)+4 -x)+4 Find: u ct 1 cot2 1 x) - 4cotx) +4 cot cor()- acot( X+ 4

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Q: 5. The volume of the solid formed by revolving the region bounded by the curve y = Vcosz, I-ax: from...

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Q: secx 7. When does the graph of the function f(x) have a horizontal tangent? 1+ tanx

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Q: Evaluate the integral dx 2x3 - 3x x |/3x - /2 2/2"V3x + v2 1 +C O 16V2 + V3 In 3 |/2 - 3x +C In +C 2...

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Q: Find the absolute maximum and minimum values of f on the set D. f(x, y) = x2 + y2 + x²y + 5, D = {(x...

A: The given question has been solved in detail Absolute Maximum value is 8 Absolute Minimum value is 2...

Q: d) Without expanding, calculate the marginal function for: TC = (2Q2 – 3Q + 7)5 %3D

A: Given

Q: e2t+a (2 cos at – 3 cosh 2at) -

A: We have to find Laplace transformation. 

Q: s(x) = X-4 Find the x-values (if any) at which the function is not continuous. Which of x2-2x-8 the ...

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Q: Which of the following graphs show a jump discontinuity? (Select all that apply)

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Q: What is the balance after 1 year in an account containing $1000 that earns a yearly nominal interest...

A: This question can be solved using the concept of compound interest.

Q: dx Given: 2x-3xlnx Find: du dx 3 dx dx dx

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Q: 1 3. Let f(x, y, z) = Show that Vx2 + y² + z²° frx + fyy + fz2 = 0.

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Q: z° – 6z' + 4z – 2 dz |

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and indica...

A: Question: Find the absolute maximum value of the function over the indicated interval and indicate t...