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Q: Find the arc length parameter along the given curve from the point where t=0 by evaluating the…

A: We have to find the arc length.

Q: Prove the following identity: 1- tan? e cos 20 = sec e

A: solution:-cos2θ=1-tan2θsec2θ RHS=1-tan2θsec2θ        =1-sinθcosθ21cosθ2,      ∴tanθ=sinθcosθ &…

Q: a. V80.5 ; where: V81 = 3

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Q: For the curve defined by *(t) = 2 cos(t)i +2 sin(t)j + 3tk evaluate F (2)||du S = to find the arc…

A: Given that the curve  r→t = 2 costi→ + 2 sintj→ +3tk→  = f(t)i→+g(t)j→+ h(t)k→        we  have to…

Q: 2x dx 4e2x –8eª +5 e

A: To evaluate: I=∫e2x4e2x-8ex+5dx=∫(ex)24(ex)2-8ex+4+1dx=∫ex4((ex)2-2ex+1)+1dx=∫ex4(ex-1)2+1dx

Q: 6s – 4 s2 – 4s + 20

A: 6s-4s2-4s+20=6s-4s2-4s+4+16=6s-12+8s-22+16=6(s-2)+8s-22+16=6·(s-2)s-22+(4)2+8·1s-22+16

Q: Use the method of cylindrical shells (do not use any other method) to find the volume of the solid…

A: Volume of solid bounded by y=f(x), x axis and  x=a to b is given by below:

Q: Integrate 7 dx , 1+ Vx+1 3

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Q: sec(2) tan(2) – 1 dz 3.

A:

Q: Set A: Problem # 6 Fnd the eaquation of the line tangent to FG) = cos?x- sin*G) sin ) at

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Q: c2 1 dx x² +1 4. e* + 0.

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Q: 9. Determine the points of inflection and discuss the concavity of the graph of f (x) = x* – 4x²

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Q: set D: Problem #G Find the eauation OF the Iine tangent to F Cx) = cos? x - Sin? (x) at X 3r %3D 4

A: To find the equation of the tangent line at x=3pi/4.

Q: Use (a) bisection method and (b) false position method to find the solution to the following within…

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

Q: Consider the function g defined by g(x, y) = sin (T /Ty) + log3 (x – 3y) Do as indicated. 1.…

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Q: What is the farthest point on the sphere x2 + y2 + z2 = 16 from the point (2

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Q: A cross section of a nuclear cooling tower is a hyperbola with the equation y? - = 1 902 1302 The…

A: Solved below

Q: x = -2t Given: line l1 : 3 1 – y = Z - 8 and l2 y = 2 + 2t z = 6 + 2t %3D 1. If the given lines…

A: The solution is given in the next step.

Q: 5. Find the directional derivative of f (x, y, z) = e* cos(xyz) the point (1,- 2.0) in the direction…

A: On solving this we will get

Q: X=34-3 X=2-2y (-3,0) 12,07 y = 2X-4 -4 49-3

A:

Q: In each part, evaluate the integral, given that SIx - 61, x 2 0 f(x) : x + 6, x < 0 ' %3D

A: The solution is given in the next steps.

Q: Find, the genetal Solution of the differehtial equation (2x+Y-3) dy= (f+2Y-3)dX

A: Given problem:- Find the general Solution of the differential equation   (2x + y - 3) dy = (x + 2y -…

Q: 1. Find the equation of the plane containing the lines L1 and L2 given below: z = 4t + 3 z = -4s – 1…

A: Given :L1:  x=2t+1, y=3t+2, z=4t+3L2 : x=s+2, y=2s+4, z=-4s-1

Q: The following question is about the rational function (x + 1)(x - 2) rex) = (x + 2)(x – 6) The…

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Q: Mary, Martha and Lazarus lives in the same house. It takes Mary 2 h to clean the house alone. Martha…

A:

Q: Зх-7 dx 10x2+3x+11

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Q: Using Linear Approximation, determine the approximate value of the following: Final answers must be…

A:

Q: Triangle BAC is a 30°°-60°°-90°° right triangle. 600 30° A C If BC = 15, what is the measure of AC?…

A:

Q: B. For each of the following functions z, find az az a2z and дх? дудх" дхду ay2 1. z = 2x? – 5xy +…

A: We know that when we differentiate a function partially with respect to 'x' , other variables of…

Q: Find, the genetal Solution o the differehtial equation (2x+Y-3) dy= +2Y-3)dXf %3D

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Q: Use Lagrange Multipliers to solve the following: Maximize f(x, y, z) = 4x + 2y + z subject to r? + y…

A: Given

Q: The average amount of time that a customer waits in line for service is given by W(x, y) = y < x…

A:

Q: Find the Inverse Laplace of the following 6s – 4 s2 – 4s + 20 2e-24 cos 4t + 8e " sin4t Option 3…

A: Explanation of the answer is as follows

Q: E2"x" 4η n 7. it. n=0

A: The objective is to find interval of convergence and radius of convergence.

Q: Find the minimum and maximum values of the function y = 8Vx? +1 – 5x on the interval [0, 3] by…

A: To find the minimum and maximum values of the function y=8x2+1-5x on the interval 0, 3 by comparing…

Q: NONHOMOGENEOUS EQUATIONS: UNDETERMINED COEFFICIENTS  2. (D^2+D-2)y=2x-40cos2x Please answer this…

A: Here, the given DE is: (D2+D-2)y=2x-40cos 2x Now, to find the yh. The auxiliary equation of the…

Q: Solve the equation on the interval 0s0< 2n. 8 cos 20 = 4 What are the solutions in the interval 0s0<…

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Q: 4s + 12 s2 + 8s + 10 4e -4t – 4te -4t 4e4 + 4te4t Option 3 Option 2 -4t 4e + 4te¬4t

A:

Q: 9. Determine the points of inflection and discuss the concavity of the graph of f (x) = x* – 4x²

A: Given : f(x) = x⁴ - 4x²    -----(i) We have to find point of inflection and the concavity of the…

Q: 1. 3p² tan¯p dp

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Q: Using Linear Approximation, determine the approximate value of the following: Final answers must be…

A: Topic:- application of derivatives

Q: '9 — х? dx x2

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Q: Find dy/dx if ylnx + y^2 = 0.

A: According to our guidelines, we can answer only one question or three subparts of a question.

Q: VI. Determine all the relative minimum and maximum values, and saddle point/s (if any) of the…

A: Given,  h(x,y)=x3-3x+3xy2

Q: Company data suggest that the total cost of a certain flight is approximately C(x) = 120x – 0.38x +…

A: This is marginal cost finding question.  We can find the marginal cost by differentiating the…

Q: Current Attempt in Progress Evaluate the definite integral two ways: first by a u-substitution in…

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Q: Acos'e -3=-4cos0

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Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (- 3, 4, 3), Q = (6, 6,…

A: .

Q: 4. If f is a differentiable function of a and y with w f(x, y), x =r cos 0 and y = r sin 0, %3D show…

A: To verify the given relations between partial derivatives.