(c)m Prove that: √ [e¯`‚F₁ (a:c:x)]=(−1)″ (c − a) „‚¤¯* ₁F₁ (a;c+m;x).

Q: Let f(x) = {ax² (2x + b differentiable (a) 1 at x = 1. x ≤ 1 x>1 (b)-1 . Find a so that f is (c) 2…

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Q: Define F : R → R and G : R → Z by the following formulas: F(x) = (x^2)/3 and G(x) = ⌊x⌋ for every x…

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Q: What is true about the function f(x) = a) f(x) → 2 from below

A: Introduction: When a variable approaches its limit from the right, the function's right-hand limit…

Q: a) f(AUB) = f(A) U ƒ(B). b) (i) f(An B) ≤ f(A)n ƒ(B). (ii) Find a function f {1,2} → {a}, and A, B C…

A: a)  We  have  to prove  that  Now,      Thus,  (Proved)[since, b) i) We  have  to show  that Let  be…

Q: The Domain of f (x) = V1 – x is 1. [-1, 0) 2. (-∞, 1] 3. (-0, 1) 4. [1, c0)

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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: 11 11 For f(x) = x" and g(x) = 'Vx, find (f o g)(x) and (g o f)(x). Then determine whether (fo g)(x)…

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Q: Suppose that f: R (0, ∞) and that f'(x) = f(x) ‡ 0. Prove that (f-¹)(x) = 1/x for x > 0.

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Q: Use the table to determine Df(g(x))) at x = 3. |1 2 3 4 f(x) 1 f(x) |3 -5 1 4 4 1 3 4 3 2 g(x) 2…

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Q: Prove that F (3.x)(A → B) → (Vx)A → (3x)B. 3.

A: To prove: ⊢∃xA→B→∀xA→∃xB

Q: Find f(2021) if function f satisfies following conditions: f(1)=1, f(x+y)=f(x)+f(y), for all x,y…

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Q: • The Doman of f(x) = 4 – Vx is 1. (2, 0) 2. [-2,0) 3. [2, 00) 4. [-2,2]

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Q: 11. Let f(x) be any function with the domain (-o, 0). a) Let e(x) = @)+f(-x), Verify that e(r) is an…

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Q: Q1] (A) If F(x+y-z₁x² + y²)=0 where z = z(x, y) дz дz x -y =x-y ax (B) If f(x, t) = f²e-y²dy, then…

A: (.)  Leibniz rule :      Given ,(A).        where   and   .(B).

Q: 2 Iƒ ƒn(x) = efn−1(x) for all ne N and fo If d nd {ƒn(x)}. dx

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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: Let the function f:R-->R be twice differentiable and suppose that f(x)≤0 and f''(x)≥0 for all x.…

A: It is given that, the function f:R-->R be twice differentiable and suppose that f(x)≤0 and…

Q: LET • (CX)= In [x²(x+5) ³ (x² + 4)⁰7 f'(x) = LET F(x) = \n [X²(X + 3) ³ (X² + 2)²] Cico

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Q: 3 prove that sinh (2) isine

A: Since you have posted multiple questions, we will provide the  solution   only to the first question…

Q: show the function is continous dis continou or 2=(2x+3 3メ→1」Xハz F(x)ニ

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Syppose that Ts Cx) centered at a for f(x) is giver by T5 (x) = 3+5(x-2) +8(x-a)?+a(x-2)+ (x-2)5.…

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Q: Prove algebraically that  A+A'B'=A+B'

A: We have to prove algebraically that  A + A'B' = A + B' We know that, the distributive property  A +…