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

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Q: Show that F(s) est ds if F(s) for ->O as $18 t>o

A: According to the question,

Q: 3. Find [g f](x) for f(a) = 2x +5 g(2) = 2 – 3. and

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Q: determine L−1[F].

A:

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: 2- Find f(t) for F(s) = s+4s+20

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Q: The interval on which f(x) = 3 – 2x – 12x² – x³ is | - concave down is: O (-4, 0) O (-∞, 4) O (4,…

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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: 5. f(x)= 3x - 2 Laukit O x 6. f(x) = [2x + 1] L LUGA I dad

A: The objective of the question is graphing the given functions.

Q: h(x) = Vx – 2 on the domain [2, 5]. -

A: The given graph is:

Q: Suppose that f'(t)-29 (b)31 (e)none of these

A: Given: Suppose that f'(t)<3 for all t in R and f(3)=1. To find: f(-7)  Lagrange’s mean value…

Q: B.1. Consider the function f: NR given by 4n • ( [47] - √₂). 3 f(n) = n Prove that f(n) is O(n²).

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

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Q: 15. The number of points where f(x) = |x|² - 3|x|+2 | is not differentiable is/are (C) 4 (D) 1 (A) 5…

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Q: 3. (a) Find a unit in Z[√2] which is not equal to 1 or -1. Hint: Use 1 (b). (b) (*) Show that Z[√2]…

A: The objective of the question is two-fold. First, we need to find a unit in the ring Z[sqrt(2)] that…

Q: The degree of the differential equation dx (割()). +sin dy +1=0is: dx dx Select one: O A. 2 О в. О O…

A: Degree of a differential equation: Order of a differential equation is the order of the highest…

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

A:

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: 8. Which of the following statements about the asymptotic behavior of f(n), g(n), and h(n) is true?…

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Q: 12. Let f(z) =,h z 0. Then f(2 + h) – S(2) h A) – 4+ 2h 1 B)- 4+ 2h C)-- 4- 2h 4-2h

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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: 14. Let f(n) = n² + 20 and g(n) = n³. Show that f(n) is O(g(n)) by finding a positive integer N for…

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Q: (iv) p(39), where p is the Euler p-function.

A: Euler totient function and residue classes

Q: 6. Let f(x) = V2x + 1, find as Ax - Ax

A: