Find if possible the limit of the following sequence: x[k] = ,k = 1, 2, 3, . The limit is (Type an integer or a simplified fraction, or N if the sequence diverges.)

Q: Given the linear differential equation: y'' - y = cos(x) - 5sin(2x) Find the general solution…

A: Solving

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(In 12x) dx Cos In x +…

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Q: Find the work done in pushing a car a distance of 12 m while exerting a constant force of 300 N.

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

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Q: For the series below, (a) find the series' radius and interval of convergence. For what values of x…

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Q: Find the first partial derivatives with respect to x, y, and z. 7xz x+y

A: This question is related to differentiation, We will solve it using given information.

Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 4 sin(x). If f(0) = 2 and f'(0)…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 3…

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Q: Describe the graph of the equation. r - 12cosri + 5sinsj -k O tis an ellipse in the z = -1 plane,…

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Q: Find V (V x F), if F(r, y, z) = 7e""i + 2xe"j- 3e""k.

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Q: The distance traveled in the time interval 0 <t < 4 is given by the following. -4 r4 |t2 + 6t – 16|…

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Q: S Vcos 20 sin 20 do

A: To evaluate the following integral.∫cos2θ sin2θ dθ

Q: 5. By Chain Rule , evaluate b. y' for y = u² + 2u and u = x² + 2 %3D

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Q: You are given the following information about a termite colony population. The current population is…

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Q: Let f (x, y, z) = xyz. Determine the value of fryy + fyay – 2 fyyr Simplify your answers.

A: We have to find the value.

Q: Use series to approximate the value of the integral with an error of magnitude less than 10-8. 0.19…

A: We will use atleast 8 digits in every value which eventually lead to the error less than 10-8.

Q: Integral

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Q: Find the first derivative of the function below: f(x) = (cos(2a – 7))sin(z+1) %3D

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Q: Use the divergence theorem to find the outward flux of the vector field F(x,y,z)=3x2i+1y2j+2z2k…

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Q: Consider f(x) = (5x + 11)2022, find: i. f'(x) ii. f"(x) iii. f''(x)

A: Given Data: f(x)=5x+112022 Formula used: dax+bndx=nax+bn-1dax+bdx dxndx=nxn-1

Q: Find the equation which satisfies the separable differential equation dy – 18x dx with the initial…

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Q: 2. y = [log(arccotx³)]coshx. Find dy/dx

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Q: [x+1

A: The objective of the question is evaluate the indefinite integral.     Note -  As per our guidelines…

Q: Question 6 Determine the derivative, y': y = log, (In a?) %3D Oy = z In 5 In a Oy = = z In 5 In z Oy…

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Q: 3. [sinh ot e"dt Ans.

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

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Q: Find the arc length of the graph of r(t) eV2li +e¬V2lj+2tk, 0<t< v2 ln 9 NOTE: Enter the exact…

A: Given problem:-

Q: plapii the function f(t) = 6t(h(t – 1) – h(t – 6)) for 0<t<o. Use your graph to write this function…

A: Heavyside function

Q: 3 Evaluate the following indefinite integral: 1.) f 10ma dx

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Q: 2. (Section 9.2) A refinery produces both gasoline and fuel oil, and sells the gasoline for $4.00…

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Q: Question 3 Determine the derivative of In(csc x) cot x Csc I - cot x CS z Previous

A: A detailed solution is given below

Q: Find V· (F x G), if F(x, y, z) = 6xi+j+15yk and G(x, y, z) = xi + yj – zk. V · (F × G) =

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 5ytx²j+4z² div F= curl F=

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Q: Find the intervals on which f is increasing and decreasing. f(x) = - 3x + 2x2 + 7 On which…

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Q: Find y': y = ar cos

A: The given function,  y=ar cosx3

Q: Which among the following is false for getting the derivative of an implicit function? O Another way…

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Q: Evaluate: 3 A 1–x*) 2 + C 3 (1-x*) ² + C --(1-x*) ² +C D 1-x*) 2 + C 3

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x + 3 lim x--3 x + 27

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Q: Find the indefinite integral. (Use C for the constant of integration.) 5 tan(7x) sec2(7x) dx

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Q: Evaluate (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (5, -5)

A: The objective of the question is evaluate the definite integral.

Q: The most conveneient way to evaluate x2- by substitution is to let Vx2- 4 =y A True B) False

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Q: Represent the following equations in R? by a vector-valued functions. Imet gaoglecomis shwing your n…

A: Given

Q: Determine the derivative of the following curve: T3+y3 +yi = 5

A: Given: x23+y23=5

Q: Ir(t) - u(t)] and Ir(t) x u(t)] in two different ways. dt r(t) = cos ti + sin tj + tk, u(t) = j + tk…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise.…

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Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Sh dx

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: Find curl (4z i+ 5x j+ 9y k). curl (4z i + 5x j + 9y k) = ( Di + ( j + ( i i )k

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Q: Evaluate the integral. (5 – 2t + 3t2) dt |

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Q: S(1 – 2x²)(x + 3)dx

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