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

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Q: Given the points A(-2, 3, 1), B(0, 0, 2), and C(-1, 5, -2) Determine ZBAC, the angle between AB and…

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Q: A particle is moving with acceleration given by the function a(t) = sin t - 3t. Find the position…

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

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Q: dx Vx-4x-7 S- -dy y2-8y+5

A: The given integrals are' 1)1/sqrt(x2-4x-7)  2)7/(y2-8y+5).

Q: In the equationf (x) = e* In(11x) – e**+* + log(e6x*), find f '(3). %| -

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Q: 2x e dx 4e2a –8e* +5 -

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Q: Show

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Q: Topic on Application of Integration - Area. Find the point/s of intersection of the graph and draw…

A: Here point of intersection of the line y=0 and y=x2-4 is put y=0 x2-4=0x2=4taking square root on…

Q: 4. Find (a) the gradient of f at P and (b) the rate of change of the function value in the direction…

A: A detailed solution is given below.

Q: Find the vector of length v7 in the direction of AB + AC

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

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Q: 11. A spherical balloon is inflated so that its radius (r) increases at a rate of (2/r) cm/sec. How…

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Q: 2. For the parametric equation shown below, determine the value of (dy/dx) and (d²y/dx²). x = 3t? –…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

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: dx Vx²-4x-7 7. dy y2-8y+5

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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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Q: 8x + 1 10. Evaluate the integral / dx. 4.x2 + 12x + 10 11 (a) In |4.x2 + 12x + 10|| tan-(2x + 3) + C…

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Q: 3 Use the linear approximation to estimate Af = f(3.1) – f(3) for f(x) = I+x (Use decimal notation.…

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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: S 3p? tan" p dp

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Q: (t- 1)* 24 24 4 24 24 4 1 85 84 g5 84 82 O Option 1 O Option 2 24 24s 12s² + 4s3 + s4 12s2 + 4s3 + s…

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Q: . L'Hôpitaľ's Rule Evaluate the following limits or explain why they don't exist. 1 lim 1 X→0 sin x

A: Rewrite

Q: 2eln In cos 2t 8 + 2 None of the choices Option 2 2s s2 – 2 s2 – 2 Option 5 Option 3

A: This question is based on Laplace transform.

Q: Use a calculator to find the approximate value of the expression. Round the answer to two decimal…

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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: f 3p2tanip dp

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Q: I. Evaluate each of the following iterated integrals. T/2 siny 1. dxdy

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Q: nt Use the model A Pe" or A P where A is the future value of P dollars invested at interest %3D…

A: Let's find.

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: d of Variation of Parameters: [D² - 8D + 16]y = e4%sec2 %3D

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Q: 2. Suppose a wire three feet log is to be cut into two pieces, with each piece to be formed into a…

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Q: (6) Use the linear approximation of the following (Answers are to be expressed in 4 decimal places.)…

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Q: 1 1 1 dx x+2, x+1

A: We can solve this as follows:

Q: the function f(x) = xe-* is concave upward on Select one: O (-00, 2) O (2, co0) O (-00, 1) O (1, 0)…

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Q: (c) Let f(x) = In(x + 8). (i) Find the domain and range of the function. (ii) Find the inverse of…

A: Let's find.

Q: Find the Laplace Transform of the functions 1. e-2t (cos t + 3 sin t)

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: Σ Suppose the Maclaurin series f(x) is f(x) =£ n=0 Find the Maclaurin series for the following.…

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Q: 1 dx, if possible. State whether the integral converges or diverges. 4

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

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Q: For the function f(x) = xe-2x give intervals of increase/decrease and intervals of concavity.…

A: Let's find.

Q: Part 2. Use the integration techniques to solve for the anti-derivative of each fur I. S3p? tan p dp…

A: According to the company rule we can answer only the first question and rest can be reposted.

Q: I. Find əx and and (whenever possible) for the following functions. az ne ду 1) w%3D 5x*у — 11ху3 +…

A: 2). The given function is: w=2ytan2x+y-3xsecx2y3   As we know that; The Power law: ddxxn=nxn-1 The…

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

A: Given

Q: 4. 25t 1 dt

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Q: Evaluate sin (44o) + cos (29o) using differentials. Refer to special triangles.

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Q: The approximate value of -31.8 using linear approximation, O -1.0075 O -2.0025 O -1.9975 O (E) None…

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Q: y" + y= tanx

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

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Q: ans the space provided before each number. 1. What trigonometric ratio can we use to solve for the…

A: We have to solve above triangle problem