Q2 The following graph shows the position function r(t) of a mass attached to a spring. Note that there is no damping present. (a) Write this function in the form z(t) = A cos(wt – 4). In other words, read off A, w, and o from the graph. (b) Suppose the mass weighs 1 kg. Find the value of the spring constant k. (c) What is the maximum velocity attained by the mass?

Q: 6. Evaluate the integral /: a sec (x²) tan(x²)d.x. sec*(x²) tan(x²)d.x. sec (x²) tan(x²) (a) + C 6.…

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Q: Find the general form of the equation of the plane containing the point Q(0, –2, 10) and the lin…

A: Given: Q=0,-2,10l1:x=1, y=2t-3,z=5-t

Q: Show that - 8. ==1+* +4++++1=

A: We know ∑1n2=π26  Hence, ∑1(2n)2+∑1(2n+1)2=π26 Therefore, 14∑1n2+∑1(2n+1)2=π26 ∑1(2n+1)2=π26 - π224…

Q: Convert to a rectangular coordinate. Convert to a polar coordinates. 5T 10. 11. (-4,4)

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Q: 1. Given the vector ū = (2,0, 1). (a) Solve for the value of a so that ữ and i = (a, 2, a) form a…

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Q: Determine dydx of function g 1 g(x, y) = cos (Tx ) + log3 (x – y)

A: We will use simple differentiation rules to solve this question.

Q: Find the limit 1-ex lim x+0 10x2 – 18x

A: Here we have to use the concept of limit.

Q: Find the area of the plane region bounded by the given curves: y= x^3, y= x + 6, and 2y+2 = 0

A: Explanation of the answer is as follows

Q: 3. For each of the following functions z, find and дудх' дхду 3. z = tan-

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Q: 2. Which of the following is a valid trigonometric substitution? (a) If an integral contains 9- 4r2,…

A: Here, to find the valid trigonometric substitution.

Q: Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 5+x2 (Use decimal…

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Q: Obtain the differential equations satisfied by the given particular solution 2. y = 7- 2x +e* 3 1-…

A: Hi there! Thank you for your question. Unfortunately as per our guidelines we are restricted to…

Q: Use trigonometric substitution to find or evaluate the integral. (Use C for the constant of…

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Q: 6. The length of a rectangular yard is measured to be 84 feet and the width to be 36 feet. If the…

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Q: Convert to degrees and write it as the least possible positive coterminal angle. a. -220° b. 120° C.…

A: We have to find the angle

Q: xチ+1=4 DIDX= 2-2y (ost) X= 3サ-3 *キーに h で3,0) サ=2メー オー×ポーカ toノー4) メッとナ+ム メーリー3

A: Explanation of the answer is as follows

Q: Evaluate the following integrals using Trigonometric Substitution: 1. X-1- 16x dx

A: integration using substitution

Q: Encounter the critical points of f(x, y) = 16x3 - 9y2 - 36x2 - 12y + 6x - 27 and then denote each…

A: To find out the critical points and denote it's nature.

Q: 2 sinh x Calculate the integral, J dx. 5+ 6 cosh x

A: Given :∫2sinhx5+6coshxdx

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A: Note: There are multiple questions. Few questions has multiple subparts.No specific question has…

Q: mine the value(s) of x where the slope of the tangent line is horizontal. Use exact valı…

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Q: Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 5+x (Use decimal…

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Q: Use Method of Variation of Parameters: [D² - 8D + 16]y = e4Xsec2x

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Q: a. Lim x2 + X - 2 X→1 2x2 - x – 1

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Q: 2y(x? — у + х)dx — (x2 — 2у) dy %3D 0

A: I think mistake in question inplace of -ve sign.

Q: 3. Which of the following is a true statementCirclc all that apply. (a) If lim an = 0, then the…

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Q: To find two real numbers whose difference is 24 and whose product is minimum, we can find the…

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Q: A. For each of the following functions z, find and дх 2. z = tan 出一郎

A: Explanation of the answer is as follows

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Q: Exercise 4. Calculate the convergence set of the following is not enough, a justification is also…

A: Given

Q: "Definite Integrals" 1. sin | COS dr -

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Q: II. Let f(x, y, z) = z° sin a + Determine 2 dydzərəz'

A: We know, ∂2f∂y∂x=∂∂y∂f∂x

Q: Q.1) The general solution of the equation y e' cosA a) y(t) =c, +c; x +c,¢ ' de' cosa Re' sinx b) y…

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Q: 1 -dx. State whether the improper integral converges or diverges. 22 +4 Evaluate 00

A: We have to check weather the given integral is converges or diverges.

Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

A: As we know that; The expression for the volume of the cube is: V=a3    ....(1) Where a is the edge…

Q: 5. S , dz dy dx 2 c3

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Q: Find the volume oF the solid obtained by rotating about the Y- axis the region bounded by Y= x2 and…

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Q: Si cos3x cos4x dx 2 TT 6

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Q: Evaluate the indefinite integral, ſx² sinh x³ dx.

A: To evaluate: I=∫x2sinh x3dx⇒I=∫sinh x3  x2dx

Q: 10 Find the derivative f' (0) of f(x) = at х+4 O using the laws of differentiation.

A: f(x)=10x+4DIfferentiate w.r.t.xf'(x)=ddx(10x+4)Take constant outf'(x)=10ddx(1x+4)f'(x)=10ddx(x+4)-1…

Q: A = (Round to thế heares There is no solution. e the value of a. Select the correct choice below…

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Q: Solve the given initial-value problem y' + (tan.x)y = cos²x, y(0) = -1

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Q: 135 5. y = x³, y = x + 6, and 2y + 2 = 0 (Answer: S. U. u.) 4

A: Let's find.

Q: I. Find the general solution of the following: dy 2x 1.- dx y dy 2. xy dx 3. dy = (6e3x+ 1)dx

A: We have to find the general solution.     According to our guidelines we can do only one question so…

Q: x = 2 + 5 cos t Consider the parametric equations for 0<t<r. y = 8 sin t (a) Eliminate the parameter…

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Q: 3. Find the parametric equation of the line passing through the point (-1,0,3) and in the direction…

A: Parametric equation of line passing through a point x0,y0,z0 in the direction of N=a,b,c is…

Q: Determine the first derivative for each of the following functions. Remember to simplify. 2x-3x a)…

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Q: .What is the limit of the sequence an = [(n2 - 1)/(n2 + 1)]n

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Q: xVx +1 dx

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Q: dx 4x2 -8x + a a. S そ m 14cx-0+51+ s5 tom'/22 4 -2 b. I m1a(x-1)"+51-55 toni" )+c Ciln14 Cx-1)+sl+…

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