Use a change of variables (Substitution Method) to evaluate the following definite integral. Show all your work and give the answer as an exact value. sec?x dx Vtan x + 3

Q: Evaluate the line integral / (2x + 4y)dx + (2x – 9y)dy along the curve C : x = 4 cos t, y = 8 sin t…

A: Solution is given below:

Q: Let s(t) (2)a v(t) = Where does the velocity equal zero? [Hint: factor out the GCF] 4+12t2 36t be…

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Q: A particle moves vertically (in inches) along the yaxis according to the position equation s(t) = -…

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Q: (45)ds。(特)"- sa (49) 48 (xs) 1-1

A: The given integral is (x2+5x) /(x+9)1/4.

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

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Q: Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x2 b.…

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Q: Consider the quadratic function g(x)=x²-4x+36. Define a new function S(x) by S(x)=the slope of the…

A: As per our norms we have to write three multiple questions at a time kindly repost remaining…

Q: 3. Find the 23Td term of the arithmetic sequence whose common difference is d = 4 and whose first…

A: Find the 23rd term of the arithmetic sequence

Q: When the eigenvalues of a b A = 0 d are 11 = 2 and 12 = 0, what are the possible values of a and d?…

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Q: Assume that f(x)dx = 3 and g(x)dx = -2, find the following: 1. Sf(x) + g(x)]dx = 2. S12f(x) – g(x)]…

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Q: Consider three connected lakes, A, B, and C, where lake B has a volume of 2650 km, and water flows…

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Q: Approximate the point of intersection of the graphs of f and g. Then solve the equation f(x)=g(x)…

A: This question is related to Functions, we will solve it using given information.

Q: Consider f(x) = 6.9x3 + 9.1x2 - 4x + 7.7. Using the given function, approximate f(4) by making use…

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Q: Write a real word promble to compare fractions the solve the problem

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Q: arcsin = ab? x? - Va2- y2: Find y'. 2abe (+0) /a-y 1-y 2ab a 1-y 2ab a /a-y %3D

A: We neee to find derivative of y for the function given below:

Q: test conerg ence and clivergence h!

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Q: (2xy+x^2+x^4)dx - (1+x^2)dy=0 the answer should be

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Q: 8 3k - 5 Σ is equal to k=1 2 A) 46 в 38 c) 34

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Q: What is the range of the function y=f(x) =2sin 57 A [-3,7] B B [-7,-3] В © [-7,3] D D [3,7]

A: We have to find range of give function.

Q: Problem 4. Explain whether or not the following sets are subspaces of the given vector space +6] -b:…

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Q: The marginal cost for a company to produce q items is given by MC(q) = 0.002q -0.7q +620. The…

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Q: Use Lagrange multipliers to find the extreme values of the function f(x, y, z) = x² +y? + z2 subject…

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Q: Find the derivative, dy/dx: y = log3 (2x +1) Oy =- (2z+1)3 In 3 Oy = (2r+1) In 3- Oy= log, e (2z+1)3…

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Q: 11 ti + dt

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Q: For the given function find dy/dx. x- y' | = x + 2 y+ x2 1- x-3y-4x 3x2 + y + 2 y' 1- x + 3y - 4x y…

A: x-y3y+x2=x+2

Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. 2x-5 =…

A: Given data:- 2x-5 = 16

Q: Determine f„ (0, T, 1), fy(0, , 1), f¿(0, r, 1) given the function z sin(3xz+ y²)

A: The given function,        zsin3xz+y2

Q: Ty csc?y dy is equal to A у coly + | coty dy - Scony dy В у coty — Scory dy —у сoty- —у coty + coty…

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Q: Sing do Coso + Cose-2

A: LetI=∫sinθcos2θ+cosθ-2dθPut cosθ=uDifferentiate on both…

Q: Find r(t) · u(t). r(t) = (7t – 4)i + j + 4k u(t) = t?i – 8j + t?k r(t) · u(t) = Is the result a…

A: Use dot product concept

Q: Find the generating function for this when n=2, f(2)=1. n=3, f(3) = 6. n=4, f(4)= 25. n=5,…

A: Given :n=2, f(2)=1. n=3, f(3) = 6. n=4, f(4)= 25. n=5, f(5) = 125. n=6 f(6) = 750To find : The…

Q: _1. (2x – 3) dx А. —2 - _2. L (x³ + 2x) dx В. 0 _3. (x² – 2) dx С. 3 1 -

A: 1) ∫02(2x-3)dx2) ∫-11(x3+2x)dx3) ∫03(x2-2)dx

Q: Integral calculus, partial fraction decomposition

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Q: A farmer can buy two types of plant food, mix A and mix B. Each cubic yard of mix A contains 20…

A: This question can be solved using the concept of linear programming.

Q: (a) / Which of the following integrals is equal to -2+ In 2? X - 4 dx (a) 4- I dx (b) 2 - 4 da (c),…

A: To find which of the given integrals has given value

Q: The sixth term of a geometric sequence is 1215 and the third term is 45. Find the first term and the…

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Q: The marginal cost for a company to produce q items is given by MC(q) = 0.004q - 0.9q + 615. The…

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Q: Find V. (F x G), if F(x, y, z) = 3xi +j+ 10yk and G(x, y, z) = xi + yj – zk. - V. (F x G) =

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Q: (a) Use Green's Theorem to find the line integral over the simple, closed curve C : r(t) = (cos t,…

A: To use green's theorem to find the given line integral over the curve C

Q: Ex: Investigate the convergence of the following series. H.W 1 7 2) ΣΥ-1 3n 2n+5n IL !

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Q: Write down the first four terms of the sequence given by x, = 3" + 2", starting from n= 0. X1 = X2 =…

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Q: 2x (x – 3)² A = 6, B = 2 A = 2, B = 6 A = 2, B = - 6

A: The given integral is 2x/(x-3) 2.

Q: 1. Given ä = (-2,–1,4),B = (5,2,3)and č = (-3,0,5) determine each of the followin a) ĉ b) |2ã – 7|…

A: As per our guidelines we are supposed to answer?️ only 3 question. Kindly repost other question as…

Q: 5x2+11x+2 dx x(x+1)²

A: integration using partial fraction

Q: Refer to the given below. Find the indefinite integral. Simplify your final answers (Just like how…

A: i)∫(2x3+12x2-5)dx=∫2x3dx+∫12x2dx-∫5dx                                   =2∫x3dx+12∫x2dx-5∫dx…

Q: Find the derivative of the function: y = (e**)e Oy = e (e*+ + 1) Oy - (e") (e*+* +1) Oy = (e…

A: We know that derivatives of  d(xn)/dx = nxn-1. And d(ex)/dx = ex.   Here i attached the solution of…

Q: 1 2 f(t) = 3 Vi+1 2. Given SET A. determine f"(t)

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Q: A right circular cylinder has a radius increasing at the rate of 4 cm per second but its total…

A: A right circular cylinder has a radius increasing at the rate of 4 cm per second but its total…

Q: Find if possible the limit of the following sequence: x[k] = ,k = 1, 2, 3, . The limit is (Type an…

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Q: For the given function find dy/dx. = x +2

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