2. Find the Maclaurin polynomial of f (x) = cos x.

Q: 0 T/2 f(x) | 1 X -1

A: Solution-

Q: Does the function f(x) = 5x − cos(x) + 4 have a root on [−π, 0]? Justify your answer.

A: Explained below

Q: Find the third Maclaurin polynomial to f(x) = e sinx

A: The Maclaurin series; fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+.... Where the center is at x=a=0…

Q: Find f(x).

A: Given,

Q: Calculate the degree 2 Maclaurin polynomial of the function F(x) = cos(t?) dt.

A: We have to find

Q: Answer f(x) = COS T, n = 4

A: As per guideline we have to solve one question

Q: 3 Use the definition 平grien FuncTionsEat'co,): for ー X+y X-ツ ix=ツ ) fory) =) singty4) ーty2 (x) #…

A:

Q: Find the critical numbers of the function. g(x)%3D8X+sin 8x

A: Given query is to find the critical numbers for the function.

Q: Find the linearization L(x) of the function at a. f(x) = cos(x), a = 77/2 L(x) =

A:

Q: c If f" (x) = 18 cos 3x and f' (0) = f(5) = 1, find f(x).

A: The solution of the problem is given in the next step.

Q: Find the best quadratic approximation to f on the interval [ 0, 1].                   f(x) = sin(…

A:

Q: Q1/: a: Using the relation showthat J-va (x) = 2 cos x

A: We have to solve given problem:

Q: Let F(x) = | sin(7t) dt. 0, Find the MacLaurin polynomial of degree 7 for F(x). 0.71 Use this…

A:

Q: Find constants c1 and c2 such that: F(x) = c1 sin(3x) + c2x cos(3x) is an antiderivative of f(x) =…

A:

Q: 1. Find the fourth Maclaurin polynomial for f (x)= sin 2x.

A:

Q: (a) Differentiate f(x) = Vx+4 by using the first principle. (b) Differentiate the following…

A:

Q: Q1: Find the third Maclaurin polynomial to f(x) = sinx

A:

Q: Let f(x) = 2x? cos(4r). %3D f'(x) = - 8x sin(4x) + 4x cos(4x) COS f'(2) = %3D f"(x) =|| 0 f"(2) =| |

A:

Q: Given, f (x, y) = sin (x²y – 2x + 4). Find fy. - x cos (x²y – 2x + 4) x² cos (x²y – 2x + 4) O-x² cos…

A:

Q: Differentiate the function. F(t) =3 Cos2t

A: To find derivative of Ft=3cos2t

Q: Which is the best of the following polynomial approximations to cos 2x =0? near x A) 1+ % 2 1 + x C…

A: We will solve the problem

Q: Find the residue of the function: f(z)=- sin(z)

A: Given fz=2sin z To find the residue of the function

Q: Let F(x) | sin (4t?) dt. Find the MacLaurin polynomial of degree 7 for F(x). 0.8 Use this polynomial…

A:

Q: Find the nth Maclaurin polynomial for the function . f(x) = cos x, n = 4

A:

Q: Prove that the following function is harmonic and obtain its harmonic conjugate function: u(x, y)…

A: Introduction :

Q: Find the f( for this f (x) = l09, x Cos-lx

A:

Q: 1-Show that the function :defined by the base f(x, y) = x³ 3xy² - harmonic function

A:

Q: 12. V5z-8 f(z) = 13. f(x)=sin(3x² +x)

A: We can answer both the question as below using chain rule.

Q: Find the orginal function of this A Fx) =-1 (B) Frz)= X +1 ニー re Fez) s -x+3 tan x - sec3x

A:

Q: Let F(x) = sin (8t) dt. %3D Find the MacLaurin polynomial of degree 7 for F(r). 0.69 Use this…

A:

Q: Find the function f(x) such that f''(x) = 6x + 3 cos(x), f(0) = 5, and f(1) = 2 − 3 cos(1).

A:

Q: Find the quadratic approximation of f at x = 0. sin 8x f(x) = e О А. Q(x) - 8x-32х2 О В. Q(х) — 1 +…

A: Given that

Q: 2:- Find the domain of the following functions c) f(x) = sin¬'(2 – 3x) %3D

A: Solution of the problem as follows

Q: Let F(2) = | sin (6t) dt. Find the MacLaurin polynomial of degree 7 for F(x). 0.63 Use this…

A:

Q: Let F(x) = | sin (2t2) dt. Find the MacLaurin polynomial of degree 7 for F(x). 2x + 15 0.66 Use this…

A: we have to find the MacLaren's series of the given function  F(x)=∫0xsin(2t2)dt A MacLaren's series…

Q: Find f. f"(x) = cos(x), f(0) = 1, f'(0) = 8, f"(0) = 6 f(x) = sin x + 7x/2 + 7x +8|

A: We will first find the general solution of f"'(x)=cos(x)

Q: The residue of the function sinz is (z+i)3

A:

Q: Find the convolution of the two functions: f(t) = 2t and g(t) = () Cos 3 t. %3D

A:

Q: 5. (a) Find T2(x), the 2rd degree Maclaurin polynomial for f(x) = sin(e“ – 1). (b) Use T2(x) to…

A: Given f(x)=sin(ex-1)

Q: Let k be a fixed positive integer. The nth derivative of 1/(xk − 1) has the form Pn(x)/(xk − 1)n+1…

A: Given: nth derivative of 1xk-1=Pnxxk-1n+1 Find: Pn1

Q: Express the function in the form f◦g. 2. g(x) =cos2(x).

A: We need to show function as f∘g(x)

Q: Let F(z) = | sin(5t) dt. Find the MacLaurin polynomial of degree 7 for F(z). 0.69 | sin(5z*) dz. Use…

A:

Q: find for f(x) =|x| . [-x , a] - IT - .a 0.b0 T.cO 2n.dO

A: We have to solve given problem:

Q: Find and b such that the following function is continuous at x=( [x] – 2a x 0 -

A: To find the values of a and b

Q: a) Find the linearization of the function f(x) = cos(x) at a = π/2, b) Use a) to approximate…

A: (a) We have,

Q: If f is the function defined by f(x) = x + cos 2x, then f"(x) = %3D -8sin 2x O -sin 2x sin 2x 8cos…

A:

Q: Find the value of c that makes the function continuous at x = 0.

A: Given function:

Q: 2. Find the principal part with respect to x for x 0 of the infinitesimal f(x) = = Vx + Vx. (That…

A: We have to use expansion of the function after some manipulations.