+00 (-1)" The Maclaurin series expansion of tan-1I is given by tan¬ I = (2n + 1) 2n+1 for r € (-1,1). Use the sixth degree Maclaurin polynomial for r tan-l x to approximate G) tan your answer as a single fraction in lowest terms).

Q: 4. Suppose the function is defined by y = f(x) = x² – x a. Find the average rate of change of y with…

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Q: 1 31 41 В' 25' 32

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A: Given ∫02∫y4-y2 xy dx dy We will solve the first Integral ∫y4-y2 xy dx =yx22y4-y2 =(4-y2-y) (y4-y2…

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A: As per Bartleby guidelines rule I am answering only first question as both question is different and…

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Q: 21 4 B=5 -2 A= %3D 3 0 Find the Lollowing 5 Only) (chease A+B 3A -B

A: A=2-130  , B=521-21) A+B    =2-130+521-2  =2+5-1+23+10-2  =714-2A+B=[714-2]

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Q: 1. How to determine whether the function is continuous or not at a certain point?

A: As per our guideline we are supposed to be answer only one question please repost the other question…

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A: Find your answer below

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Q: 1. Which of the following series are power series? 3(х + 2)" In(n) (iii) (i) ::: 11 nx2n sin" (x) (x…

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Q: . Value of t such that vectors a=, b=, c= are coplanar.

A: Value of t such that vectors a=&lt;1, 1, 1&gt;, b=&lt;2, -4, 0&gt;, c=&lt;1, t, 3&gt; are coplanar.

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Q: Is the set Z of integers countable? Why or why not? How about the set of all odd positive integers?…

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A: We will evaluate the given integral in this question.

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A: answer is in next step

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Q: .2 f (x) = 1+ x3

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Q: Evaluate the following limit. (8x² -) lim (ху) - (6, -5) Select the correct choice below and, if…

A: In this question, we will find the limit of the function along two different paths .

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Q: Item 1. Consider the given: x³ – 4x2 8(7x – 4) (x + 2)4 х(х + 8)(х — 2) f(x) = (x + 2)2 . (x + 2)2…

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Q: 8 x2 + 16 dx x2 The integral is equal to ...

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Q: 2r – 3, Use the limit definition of derivative to show that f(x) = I 2 I = 2.

A: for differentiate at point  the function should be contineous at point for contineous limx→2+ f(x) =…

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Q: -1 1 Let: Define the linear transformation T : R³ → R² by T(#) = Az. Find the images of u = 3 and i…

A: To solve the following problem

Q: A. For each of the following functions, find the indicated derivative using the definition. 4. f(x)…

A: Let's find.

Q: (a) Find an equation of the tangent plane to the surface at the given point. x² + y2 + z? = 33, (1,…

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Q: SI sin(x) dydx. valuate the integral, show work.

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Q: Consider the given: х3 — 4х2 x(х + 8)(х — 2) (x + 2)3 8(7x – 4) f(x) = ;f"(x) (x + 2)2 i f (x) : (x…

A: The given functions and their derivatives are: f(x)=x3-4x2(x+2)2=x2(x-4)(x+2)2,…

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Q: Test the series below for convergence using the Root Test. 5 (5n + 4 2n + 1 n=1 The limit of the…

A: This is a problem related to series and sum calculation. Based on the general formula we will answer…

Q: Find Ax) if A1) =-5, and the tangent line at x has slope (3x- 1)e*-2*.

A: The tangent line at x has slope 3x-1e3x2-2x and f1=-e2

Q: 5. a. Write in your own words a definition of a complex numbers and Modulus of the complex number.…

A: This question can be solved by applying the concepts of complex numbers.