+ Is f one-to-one? is fonto? f:w→ z defined by f(n) = n! = (1) (2) (3)... (n − 1)(n) with 0!: = 1

Q: Let f:(-1,1)→ R. f(x) = (2n)! 4" (n!) ² (2n+1) -x2n+1 and f(x) = f (x), xe (-1,1). Find f n=0 -…

A: Given Information:a) ;; .b) ; .To find:The value of  in both the sequence of functions.Concept…

Q: 97 Show thet the senas- + a+/ (uhese conveages if B>« and diverges if B0, B>0)

A: Find the convergence and divergence of the given series           1+α+1β+1+α+12α+1β+12β+1+....

Q: The residue of f(2)=- (A) 1 2011! 1 (B) 2010! (C) 2010! 1 (D) 2009! 2011 at=0 is

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Q: Let f(x) = Vr - 5, g(x) = , h(a) = , Find go((gof)+h(x)) at x=-1? 2-9'

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Q: b) Given F(r, y, z) = (r³ + cosh z) i+ (2y3 – 3r*y)j – (2² + 4y²z) k. Use Gauss's theorem to…

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Q: For f : R → Rf (x) = /100 – xHow many elements of the range of f (x}are integers?

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Q: If f(x) = x² - 2x +3 when x > 1, and f(x) = x when x ≤ 1, then f(2) + f(0) = 1 Do 3 -1 2

A: Given query is to find the value of the function.

Q: 4s – 1 L-1 Is?(s+ 1)3

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Q: A = 0 0 0 1 1 1 0 01

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Q: K9. What is the end behaviour of f(x) (x + 5) (2 - x)(x − 4)? - - x →∞, y → ∞; x ⇒ − ∞, y →∞ Ox→∞, y…

A: Given: fx=x+52-xx-4 To find: End behaviour of f(x) First simplify the given function to find the end…

Q: (A) Evaluate f (4r - 5) (4/E+4r) dr. dy (B) Find if y =| + 3x - when z = 1 %3D da 6.

A: Evaluate the integral and find the derivative of y at x=1

Q: 3. Let h(x) = (f og)(x). Given f(x) = 3x2 +5 and g(x) = Vx – 3. a. Evaluate h(4). b. Determine fx).

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Q: Find R2,2(x) for f(x)

A: Given, fx=ln1+xx. We have to find R2,2x for fx. Here, R2,2x is called as Pade approximation. Pade…

Q: -3 1] Find P(A) for p(x) = x² + x – 2 where A 2.

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Q: Suppose that the functions s and t are defined for all real numbers x as follows. s(x)=3x-2 t(x)=x-4…

A: The function s and t are defined as  sx=3x-2 tx=x-4

Q: 21 -2 T 5. If B= 1 -2 T = - +4 = 2 +5 1 Using two methods to find [T]B-

A: Method I- Let T be linear transformation on  a Vector space V with n dimension with basis…

Q: O D. 2x + 2x+4 Find f(-x) when f(x) = 2x-2x+4. OA. O A. 2 +2x-4 O B. -2x +2x +4 OC. -2x + 2x-4 O O O

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Q: Evaluate L{f(t)} for if 0 < t,t + 1,t # 2 if t = 1 1 (i) f(t) = 3 -3 ift = 2 (ii) f(t) = 1 2t +1 if…

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Q: Find f(t). f(t)= *}{ 5½{/32 S s² + 8s + 17

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Q: Find f(k-1) when f(x) = 5x² + 3x + 6. OA. f(k-1)= -7K² +5k+8 OB. f(k-1)=5k2-7K+8 OC. f(k-1)=5k²-7k+…

A: Given,

Q: 1. Let N = {1, 2, 3,...} and let f: N→ N be a function given by f(x) = 2x + 3. (i) Find f(f(4) + 1).…

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Q: (–1)" >) Given: In(1 + x) = if x < 1. n + 1 n=0 2. Evaluate f(2022) (0).

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Q: . There is a function f that's continuous at 0 and f(x) = f(2x) for all x's please show that f must…

A: Answer for sub question 1a: First step is to show fx=f2-nx for each integer n≥0. If n=0: fx=f2-0x…

Q: (a) Are the following functions surjective? Justify your answers. (i) The function a : Z→ Z defined…

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Q: 3. For f(x) = 15x²-3 16x²+9x+8 As x → ∞, y → || As x →∞, y →

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Q: 1. Let f(x) = 12 + 22 + 32 + .+x². Show f(x) is 0(x³).

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Q: Let f(t) = 2t² for -4 < t <4 and extend periodically. Compute: f(1) = f(5) = f(-4.5) = f(-8)= f(12)…

A: Periodic function: A function is said to be periodic with period T if f(x+T)=f(x).

Q: Find F(s). {16e + 1) Wce - 13} (6t + 1) U(t F(s) =

A: We have to find Laplace transform of given function using Heaviside Shift Theorem.

Q: Calculate M6 for f(x) = √7x on [0,2]

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Q: 2. Let f(x) = -x– 1. a) Find f-1(x).

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Q: 3t + 2 if t 5 4 t + 2

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