Find an equation of the line tangent to the following curve at the point (a,f(a)). f(x) = 8 ex + 5x; a=0

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A: We can find the derivative as below.

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A: Given the function 1+6x-2The taylor series,1+x-2=1-2x+3x2-4x3+...... for -1<x<1

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Q: Set up, but do not evaluate, an integral for the length of the curve. xex⁹ Jo y = 0≤x≤5 dx

A: Given,  y=xex9, 0≤x≤5

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Q: Find the inverse LaPlace transform F(s) = 35+2 2 s + 25

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A: We will solve the given differential equation.

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A: Explanation of the answer is as follows

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Q: r- 24. y" +9y = 0; y(0) 25. y"-2y' + 2y = 0; 26. y" - 2y' + y = 0; 27. y"" - 4y" + 7y' - 6y=0; = 1,…

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A: Answering By observing the figure

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Q: aren't

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy - + y = f(x),…

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Q: Find the inverse LaPlace transform F(s) = 3 ²+5 2

A: Given, F(s)= 3/(s²+5) It can also be written as, F(s)= 3/(s²+(√5)²)

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A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

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A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Consider the following. u = -7i - 4j - 2k, v = 4j + 4k (a) Find the projection of u onto v. -12 2k X…

A: Given :u=-7i-4j-2kv=4j+4k

Q: 15 17' If sin 0=- where sin 20= ? OA. 30 289 cos 20= ? OA. 161 289 K <0<x, find the exact values of…

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Q: 8 20 ह n=0 77+1 A. The series converges. Its sum is B. The series diverges.

A: The objective of the question is determine the sum of the geometric series.

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Q: Find k, given f(x, y) = k(y² + xy) and [ [ f(x, y) dxdy = 54 R R=0 < x < y < 2

A: Given problem:- Find k, given f(x, y) = k(y² + xy)  And ∫∫R f(x, y) dx dy=54 where R…

Q: Evaluate Integrals [(yex - Inyx) dx

A: Follow the procedure given below.

Q: Solve the given initial-value problem. The DE is homogeneous. xy2 dy => . dx = y³ – x³, y(1) = 4

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Q: Find the limit: lim (1- cos x) sin x+0+

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Q: Find the area inside the limacon = 7+ 6 sin 0. OA) 134T - 84 B) 67T + 84 OC) 67 T OD) 134T

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Q: 3. Determine whether the sequence an = limit. x + 3 In x converges or diverges. If it converges,…

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Q: =4 Sin4n 3n A. The limit of the sequence is: B. The sequence diverges.

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Q: Determine whether the series converges or diverges. Select the correct answer. O diverges Oneither O…

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