Q 3. Find the Taylor series of f at the point c for : (a) f(x) = e", c= 2 (c) f(x) = sin x, c= T (b) f(x) = }, c = 1 (d) f(x) = cos x, c= 5

Q: (5) Consider the several variable function f(x, y, z) = xe²y + yeš + ze¬². Give a general formula…

A: The given function,   fx,y,z=xe2y+ye3z+ze-x

Q: 4. A function f has derivatives of all orders at x = 0. Let P.(x) denote the nth-degree Taylor…

A:

Q: Find f'(x) for the given f(x). (a) f(x) = x³ – 5/a + 9x¬4 f'(x) : 106 (b) f(x) = (2x + 1)0° (3x² –…

A:

Q: Show that X. dt f(x) J3 V1 + t4 is one-to-one. f'(x) = Since f'(x) O for all x, f is increasing v on…

A:

Q: Suppose that p(x)= 8 · cos(Væ +1) · evæ+1 and that q(x) is a function with p' (x) = q'(x) for every…

A: Given that  px=8⋅cosx+1ex+1

Q: Determine if = 5₁° f(x) dx is convergent or divergent when G 1 x² and find its value if convergent.…

A:

Q: Let f be a function that has s'(0) = S(0) -- derivatives of all orders on the interval (-1,1).…

A: Given the function f, that has derivatives of all order on the interval -1,1. f(0)=1,f'(0)=12,…

Q: What is the range of f(x) = cos¯¹(0)? A [-] 2 2 B [0, π] C [-1,1] D (-∞, ∞)

A:

Q: Obtain a Fourier cosine series extension of function f(x) = e² – 1 which is continuous on the…

A: Given function is, fx=ex-1, 0≤x≤1 Part(i): For Fourier cosine series fx will be extended to a even…

Q: 5. (i) Show that +C, 1+u (a) du = 2 In u(1+ u) 1 dx du , using the substitution u = x. (b) J x(1+…

A: Given,

Q: 35 x*-30 x*+3 If the Legendre polynomials P,(x) = then: 8 Find 1) S, x P,(x) dx 2) P's(-1) A) Lx*…

A: We will solve both these questions using basic knowledge of Legendre Polynomials.

Q: The derivative of f (#) cos(-2 a +a - a2 - 2 a +1) is O f (a) = (8 a° – 3 a? +2 a + 2) sin (-8 a + 3…

A:

Q: e"+e (1) V 23 + 1 dx by speculation . x=e"+e-T (2) Use (1), if necessary, to evaluate L +1 (-) de V…

A:

Q: (b) Find the value of each convergent improper integral and show why each divergent improper…

A: We need to calculate the improper integrals and then conclude it as convergent or divergent.

Q: Discuss the continuity of the function 2ху +y? f(x.y): (x, y) # (0,0)

A:

Q: Find the divergence of U=r cos(0)a-sin(0)a+2r²sin (0) a r 2cos (0) 3 cos (0) - r 3 cos (0) - 2cos…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: (a) Find the roots of the function, f(r) = r – - 1, analytically up to 3 decimal places. (b) and…

A: (a) f(x)=x6-x3-1Let x3=yf(y)=y2-y-1Here a=1,b=-1,c=-1y=-b±b2-4ac2a  =1±1+42   =1±2.2362…

Q: 80. The function f has derivatives of all orders for all real numbers with f(2) = -1, f'(2) = 4,…

A:

Q: Suppose that Xi ∼ Gamma(αi , β) independently for i = 1, . . . , N. The mgf(moment generating…

A: Introduction:It is given that Xi’s (i = 1, 2, …, N) are independent Gamma (αi, β) random variables…

Q: (b) Suppose that f(x) = 2x^2 − x^4 . Find the intervals on which f is increasing and those on which…

A: Question no. (b):Suppose that To find the intervals on which is increasing and those on which it is…

Q: (a) Let f(x) = cos(3x – 2). Find f"(x). (39) %3D (b) Let g(x) = 2***. Find g (153) (x). %3D

A: Topic = Derivative

Q: 21. If f(x) = (x² + 1) tan-(e*), then f'(0) = (A) 0 (B) - (C) (D) 1 e

A: It is observed that the function fx=x2+1tan-1ex is a product of 2 functions x2+1 and tan-1ex.…

Q: (b) Prove that sint -dt > 0 t+1 for all a > 0.

A: Given:- ∫0x sintt+1dt >0

Q: Q1 find f'(x) using (forward finite difference formula ) at x = ½ for f(x) = sin x - e* with h= 0.1,…

A: Sol

Q: 6. Find the Taylor polynomial T,(x) for the function f(x)= cosx at a="/ it to estimate cos(29780)

A:

Q: Find F

A: Given:

Q: f, (3,5) and fy (3,)us(«, y) = |and f, (3,) if f (x, y) = (b) Find x² sin(y) – Ax-3 10 CLO-2 Where A…

A: The given function is  f(x, y) = x2. siny - Ax-3

Q: (a) Determine

A:

Q: If f(z) = 6tan(z) , then f'(r) = (A) In(6) 6tan(2) (B) sec2(z) 6tan(2) (C) In(6) sec2() 6tan(z) (D)…

A:

Q: 07/ Express in the form x + jy (1) e'(x/2-j) (2) In(3 – j) (3) sin(r/4+ j2) -

A:

Q: Find the function f(a) such that f'(x) = 5 sinh(x) – 2 and f(0) = 4. a) O f(x) =-5 cosh(x) – 2 z - 1…

A: Given that f'(x)=5sinh(x)-2 and f(0)=4 To find the function f(x)