a. Write down the 5 nonzero terms of the Taylor series around the point x=0 and find f(2.1) (4 decimal) b. Find the maximum error of ln(2.1) using n = 4.

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A: This is Bernoulli type differential equation.

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A: Please post the multiple parts separately. Here I answered 1st question as per our policy.

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A: The Principal of Mathematical Induction states that if P(n) is defined for integers n, and a fixed…

Q: 2. Find the power series representation of the following functions. And then write out their I.O.C..…

A: Please post the multiple question separately. Here I answered 1st question as per our policy.

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A: We have to find the error bound of alternating series.

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Q: (b) y = 4xª+(3+51)x³+5x²-(100+1)x-400. What is the slope of the tangent on this curve at x=2.5?

A: Given curve,  y= 4x4+(3+51)x3+5x2-(100+1)x-400 To find the slope of the tangent on this curve at…

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Q: 8. PROVE: Suppose that SCR is connected, and that f : R → R is continuous. Then f(S) is connected.…

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Q: 3. Give the parametric and symmetric equations of the line that passes through the point (4,-3,5)…

A: Hint: A vector v→ is perpendicular to both a→=a1i^+a2j^+a3k^ and b→=b1i^+b2j^+b3k^ if v→=a→×b→…

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Q: Show that The Hermite polynomials can be difined by the integral representation H, (x) = (-i)"2"e**…

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Q: 52 Which expressions are equivalent to ? Choose 2 answers: 1 56 1-6 (52) -3 (5°) -8

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Q: b) Find the angle (0) between vectors between s [1, –5, 4] and t = [3,3, 3]. %3D

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Q: A closed rectangular box witha volume of 81lft' is made from two kinds of materials. The top and…

A: Given, A closed rectangular box with a volume of 81 ft3is made from two kinds of materials. The top…

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A: relationship between voltage (V)  and uniform electric field (E) can be given by  E→=-dVdr=−∇→V…

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A: To find the projection of vector v on plane P .

Q: 4. Use a comparison test to determine whether the series converges or diverges. (a) E 1+ In n In(e"…

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A: Given the matrix A=-10-4214103 so that △At=t-13 and define T:R3→R3 such that Tx=Ax (a) We have to…

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Q: Assume P (A) = .68, P (B) = .45, and P (AN B) = .25. Find P ( An I (An).

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A: This is a problem of Logic.

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A: Given integral is ∫2124arctanx6dx

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Q: d²y What is the particular solution to the differential equation x dx? dy x² with y = 0 and dy = 1…

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A: As per the policy we are providing the solutions of first three subparts. Given :  The given series…

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Q: 31 3t and y =: 1+1' Convert the parametric equations to parametric form, sketch the graph and 1+1'…

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Q: How many permutation of the letter ABCDEFGH contain the string ABC?

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Q: Find the solution. y'-y =y2ex A y = с — х с +х B y = с —х y = D y = с +x

A: The solution is given as

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A: Given differential equation is x'' + x = 4et ; x(0) = 1, x'(0) = 3

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Q: For x, y, z, w > 0, prove that (x/z)+(y/z)+(z/w)+(w/x)≥4

A: It should by x/y, instead of x/z

Q: How can you relate antiderivatives as an opposite of derivatives in your life?

A: Solution:   Antiderivatives are the inverse operations of derivatives or the backward operation…

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