I. Find the point/s of intersection of each of the following figures given below, draw element and set up the formula only to find the area. Do not compute. 1. 2. yV16-x y =x+2 x=2 2. 4. 00 4.

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

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Q: dx J V1-4x2

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Q: Integrate 1 x + 1 dx x + 1 2

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Q: dz az and ду Suppose z is a function of x and y, and tan Vy? + x2 = ze6y. Solve for

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Q: 3s + 2 4s2 + 12s + 9 4 te 궐 | O Option 1 O Option 2 4 tet e - e 2. O Option 3 O Option 4 3/14

A: Inverse laplace

Q: Question 3 (a) Find the first and second derivative of the following function, in which a and b are…

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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: -dx x2 +9 I x3 +ar-23 ton- (특) +C a. 3 b. 1 x³ t qx + 27 tam " ) + C b*3-9*+27€an )+c C. d.늘-9x- 2구…

A: Using substitution method, integration is done.

Q: 1 (s+1)(s2 +1) + cos t - sin t) + cos t – sin t) O Option 4 O Option 2 5(e-cost + sin t) 5(-e+cos t…

A: L-1{ 1/(s2 +1)(s+1)} expand it  L-1 {-s/2(s2+1) + 1/2(s2 +1) + 1/2(s+1)} L-1 s/(s2+1) = cos(t) L-1…

Q: Find the inverse transform, indicating the method used and showing the details: 2s - 10 -5s 1. s3 3s…

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Q: x3-1 dx J2+2x+5

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

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

Q: 1. For each of the following, find where the curves intersect, draw a sketch of the region, and…

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Q: 7 In the interval T, 27|the equation sin x = 8 (a) has no solutions (b) has one (and only one)…

A: Solution of (sinx)^2 = 7/8.

Q: S 23x26 + 35 + x2-16 dx x-4

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Q: c2 1 dx x² +1 4. e* + 0.

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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: Two similar-looking series are given. Test each one for convergence or divergence. 3" ( a) Σ 3" (6)…

A: To test for convergence and divergence for the given series.

Q: Given the points A(-2, 3, 1), B(0, 0, 2), and C(-1, 5, -2) Express the vector v = (3,2,7) as a sum…

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Q: t2, -8 + 3t, g(t) = l(t -6)* + 2 cos (: -). – 6)? + 2 cos (-),

A: answer is in next step

Q: Use the limit Compariso. Testidet- ermine whe ther the following serios is, convergent or…

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Q: I. Evaluate each of the following iterated integrals. clnx 2.

A: The objective is to evaluate the interated integral.

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Q: 3. A right circular cone has a base radius of 6 feet and slant height of 10 feet. If the approximate…

A: Solved below.

Q: A deli sells 720 sandwiches per day at a price of $6 each. ... A market survey shows that for every…

A: Let price reduce x times Price of deli = 6 - 0.1x Number of deli sells = 720 + 20x   Revenue

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: Find the set of all values of x at which the line 3x-y+ k = 0 is a tangent line to the curve f(x)…

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Q: Find the Laplace Transform of the functions e -2" (cost + 3 sin t) s + 5 s2 + 4s + 5 8 - 2 3 (s –…

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Q: y" + 4y= cos'x

A: Given: y"+4y=cos2x

Q: 1/3 Find the minimum and maximum values of the function y = (t – 3t2)" on the interval [-1,3] by…

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Q: Jse the linear approximation to estimate AS = f(3.1) – f(3) for f(x) = T Use decimal notation. Give…

A: Here, the given function is: f(x)=31+x2⇒f'(x)=3-1(1+x2)2(2x)=-6x(1+x2)2

Q: Convert the angle to a decimal in degrees. 78°24'17" 78°24'17" =° (Do not round until the final…

A: We have to convert an angle of 78°24'17" in degrees.    Before converting, let us see first two…

Q: For numbers 9-11: Given a circle passing through the point (5,9) with radius equal to 4. 9. Where is…

A: Explanation of the answer is as follows

Q: (3,2,4) m = i +j+k r2: А %3D (2,3,1) В %3D (4,4,1) r: A = (a) Create Vector and Parametric forms of…

A: Given problem:- r₁:  A = (3,2,4) m=i+j+k r2 : (2,3,1) B = (4,4,1)   (a) Create Vector and Parametric…

Q: dx Vx²-4x-7 7. dy y2-8y+5

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Q: A supermarket sells two brands of coffee: brand A at $p per pound and brand B at $q per pound. The…

A: Revenue = price per unit × number of units.

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

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

Q: Question 1 Determine the inverse Laplace transforms of: 2s2-5s-1 (a) (s+3)(s²+9) (b) 3s2+5s+1 (d) 3…

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Q: 10. A conical paper cup is 10 cm tall with a radius of 10 cm. The cup is being filled with water so…

A: A conical paper cup is 10 cm tall with a radius 10 cm. The cup is being filled with water so that…

Q: dr 21. (1+x²)/16 – (tan-l r)² dx e2x+2+2 22. 8. dx x2 - 6x + 25 23. 6. 24. dr J (2 - r)V - 4x +3 dr…

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Q: (x, y) = (1, –1) { 1 Show that the function f defined by f(x, y) x2 + y (x, y) # (1, –1) x + y is…

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

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Q: Use the model found above to answer this question. Using the revenue data for Jesaki Inc. for the…

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Q: dx 5x2 + 16

A: Given that a integration and we find the solution of this question by general formula of the…

Q: x = -2t 1- y = z – 8 and l2 2 - 3 Given: line lı : 4 y = 2 + 2t % = 6 + 2t 2. Find the equation of a…

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Q: plz

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

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Q: Compute the given integral. zp-

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

A: Linear approximation is an approximation of a function with the help of a linear function.  Suppose…