Prove that 2 Sin X dx 1 + cotx + cos x It tan X cos 2 x

Q: 2 8. For the telescoping series find a formula for the nth term of the sequence of (2k-1)(2k + 1)'…

A: The telescoping series ∑k=1∞22k-12k+1

Q: Use the Modified Euler method to approximate the solutions to each of the following initial-value…

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Q: J sin²(x) cos(x) dx

A: We have to evaluate ∫sin2x cos2x dx.

Q: 11. Use the comparison test to determine whether 8 k=1 2k 4k + 5 converges.

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Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral .8 So da dx x-6 x+8

A: Need to use the fundamental theorem of calculus to solve this integral.

Q: Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started…

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Q: 31. Find the volume of the solid obtained by rotating the region bounded by x=y²-2 and y=x about the…

A: Let's find volume of solid.

Q: S In (x) √xln(x)-x dx

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Q: -1-y 3) Evaluate the integral dxdzdy? 0

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Q: Find the curvature K of the curve. r(t) = etcos(t) i + etsin(t) j + et k

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Q: Choose the angle (in radian) between the following two vectors u = and U = - O 2.059 00 O None of…

A: We know that the angle between two vectors u and v is θ = cos-1 u·vuv

Q: b) Find the value(s) of z such that the angle between the vectors U₁ = and U₂ = is equal to 30°.

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Q: If then, find f'(x). O f(x) = ²* √e² + 1 dt, 2√e +1 O None of them. O Ve +1+ C O √e™ +1 e

A: Use fundamental theorem of calculus for finding the derivative

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. (Give…

A: Please see the below picture for detailed solution.

Q: a. (f+g) (x)  the problem is f(x)=3x+4; g(x)= 2x-3

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Q: Find f', f", f"" for f(x) = 3r7-4r5 + 11³.

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Q: H.W: show that the equations are homogeneous and solve: 1. (x + y)dy + (x − y)dx = 0 2. x²dy + (y² −…

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Q: FR Find the absolute maximum and absolute minimum of the function f(x) Enter an exact answer. If…

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Q: Find the length of the curve for the interval 1 ≤ x ≤ 9 3 = √ √ √ ² ³ - 1 d dt 1 Select the correct…

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Q: 10) If 2 an = 12, then lim an = 848 n=1 (A) 1 8 (A) If lim 11) Suppose an > 0. Which of the…

A: Note:Our guidelines we are supposed to answer only one question. Kindly repost other question as the…

Q: Find the radius of convergence for Σ (sin²n)x". n=1

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Q: (d²4)(d-2)y=0

A: To find the roots of  (d2 - 4)(d - 2)y = 0.

Q: S HENN -dx x4-4

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Q: O Evaluate Je*+1 dx

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: 30. Find the area bounded by the curve 5y²=16x and the curve y²=8x-24. A. 36 B. 25 C. 16 D. 14

A: Topic = Area

Q: Find all solutions of the equation in the interval [0, 2π). 2sin6θcos2θ - 2cos6θsin2θ = - √2 Write…

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Q: SC₁+ Fuj³d₂ dn

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Q: Given that ∞ Σ n=0 x = 1 to x = - X ∞ n=0 Identify its interval of convergence. The series is…

A: Here, we know that the power series of 11-x is: 11-x=∑n=0∞xn...(1)

Q: True or False: We have Select one: O True O False 8 [√x dx √xdx = 12.

A: We have to find the given value of integration is true or false.

Q: If y, and Y2 are linearly independent solutions of y" + 3y + (5 + t)y = 0 and if W(y₁, y2)(1) = 3,…

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Q: Determine the point on the curve y = 19x² closest to the point (0, 5) with x>0. What is the slope of…

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Q: What rate of interest compounded annually is the same as the rate of interest of 8% compounded…

A: . What rate of interest compounded annually is the same as the rate of interest of 8% compounded…

Q: y' = x - 4xy

A: We have to find solution of differential equation.

Q: Problem 1. Solve these integrals using substitution (a) [ x(x r(x - 2)5dx, (b) [te²³² test dt.

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Q: A fast-food restaurant has a cost of production C(x) = 14x + 160 and a revenue function R(x) = 6x.…

A: Sol Cx=14x+160,R(x)=6xHence , Profit Function P(x) = R(x)-C(x)

Q: Which of the following is the equation of a sphere with radius r = 3 centered at the point…

A: Given that radius of the sphere is 3 and the center of the sphere is -1,0,-2. We have to find the…

Q: Find the derivative of the logarithmic functions: y = ln(12x-4)

A: Solution of given question is written in below steps.

Q: 3 A line passes through the point (-6, 4) and has a slope of 2 Write an equation in slope-intercept…

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Q: True or False: We have Select one: O True O False 0 8 √xdx = 12.

A: Let's solve given integral.

Q: A rectangular lot has an area of 1600 sq m. find the least amount of fence that could be used to…

A: Solution of given question is written in below steps.

Q: / Find Lim X. tan' 2 X X-100

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Q: Find an equation of the tangent line to the curve at the given point. y (4,16) (Express numbers in…

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Q: Ted's Machine Shop purchased a computer to use in tuning engines. To finance the purchase, the…

A: topic - compound interest

Q: Find T(t), N(t), aT, and aN at the given time t for the curve r(t). (Give your answers correct to 3…

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Q: 4T (2n)-T(n) 4. Use Simpson's rule to approximate I'v = 3 2x3³ +23dx with S(40). Use the formula…

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Q: 2. Find the area of the region inside the cardioids r = a(1+cos 0), a>0

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Q: Consider the point P(-2, 1, 4) and the vectors Question 2 a = and b =. (a) Find the unit vector u…

A: This question can be solved using the concept of three dimensional geometry.

Q: If a = (-1, 1, 2) and b = (1,3,1), then which of the following gives |ab|? Select one: O √9 O -√9 O…

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Q: ·S In (x) vxln(x)-x X dx

A: We know that integration power rule is - Integration of xn is xn+1/n+1 + C . Here C is integration…

Q: plz provide answer for question asap

A: Please see the below picture for detailed solution.