Find the Taylor series generated by fat x = a. 3 f(x) = a = 1

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A: Given:      ∑k=1∞116k2+8k-3 The series converges.  

Q: Evaluate the following integral by using substitution ∫4x/√(x^2+1) dx   limit: 0 to √48

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Q: If f(x) = 2 tan '(5 sin(3r)), f'(x)-

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Q: Given f: [2, )IR, prove that fn (x) = けx" It, converger uni formly to f6)-o.

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Q: k V9k² +1]

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Q: Consider the differential equation = (3 - y)cos x. Let y = f(x) be the particular solution to the di...

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Q: Consider the following function. +] - 2x + 2 3 2 (a) Find y'-f"(x). "(x) = (b) Find the critical val...

A: Topic = Derivative As per guidelines , At  a time only three sub-parts can be answered.

Q: Find f-(x, y, z) in the function f(x, y, z) = a?y*z + ay +? +1. %3D A. fa(x, Y, z) = 4x²y°z* + x %3D...

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Q: Calculate the integral. (Use symbolic notation and fractions where needed.) - sinh(15x) dx = +C

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Q: When x is less than or equal to 2, what equation is shown in the graph? a. f(x) = | x - 1 | b. f(x)...

A: Given question:- When x is less than or equal to 2, what equation is shown in the graph.

Q: Plot P(2, -4, 1) and Q(0, 3, 4) on the same set of coordinate axes

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Q: For the linear function y = f(x) = 3x + 10: df at I dr a. Find -7. f'(-7) = b. Find a formula for I ...

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Q: If f(x) = cos(x) Osxs 31/4 evaluate the Riemann sum with n = 6, taking the sample points to be left ...

A: Given:- f(x) = cos(x)  , 0≤ x≤ 3π/4  To find:- Evaluate the Riemann sum with n = 6 taking the sample...

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Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a grap...

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Q: Given the function: f(x,y, z) = x°y2² + æy° +y°z Find а. fazy: (x, y, z) b. fazyz(1, –1, 1) -

A: Given the function :  f(x,y,z) = x3y5z7 + xy2 + y3z

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Q: arctan dx

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Q: 6) lim Vx 0+ f (x) f (x) -0.5 0.5 -0.1 0.1 -0.01 0.01 -0.001 0.001 -0.0001 0.0001

A: 6)limx→0x

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Q: 1. f(x)=sqrt(x-5);x≠5 and g(x)=x+3. find the domain of (gof)(x) a. all real numbers greater than 5 ...

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Q: A ship carrying 1000 passengers is wrecked on a small island from which the passengers are never res...

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Q: Determine the general solutions of the following non homogenous linear equations. 1. (D² + D)y = sin...

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Q: Let f : R → R be a function such that |f (x) – f(y)| 0. Write the e-d definition of continuous func...

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Q: Let f(x) = tan '(sin(2a)) f'(r)

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Q: The graph of f (x) is given by 3 Determine the following limits. Write your answer in the form lim f...

A: The graph of the function fx is given by Condition for the limit to exist:  limx→c-fx = limx→c+fx T...

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Q: 10) Determine whether the series converges or diverges. 5 2'n!

A: Ratio Test :Suppose we have the series  ∑n=1∞an , Define,                L = limn→∞ an+1anThen,(i) I...

Q: Let (M; d) be a metric space. Show that the set {B(x; 1=n); x ∈ M; n ∈ N*} is a Basis for the metric...

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Q: Which term best describes the mapping shown? a. relation b. function c. one to one function

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Q: Find all solutions of the equation in interval [0,2pi). 6sin^2(x) = 6+3cos(x)

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Q: The following is the graph of a function f(x). 4 3+ 2+ 1- 1, -1 -1- -5 -4 -3 -2 4 -2 -4 -5- Clear Al...

A: Graph of f^-1(x) is symmetrical about line y=x.

Q: Let f(x, y)= Jxy +x+xcos y. (a) Find fxy.

A: Given:  Let fx, y=xy+x+x cos y To Find:  To determine fxy.    

Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y ...

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Q: Let g(x) = x². Which of the following outputs of g is not guaranteed by the Intermediate Value Theor...

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Q: dy re: (e + e-")- = y² (separation of variables) da

A: Given that: (ex+e-x)dydx=y2

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Q: (a) Determine all distinct values of vZA given that A = -1+ iv3.

A: Follow the procedure given below.