Let (x₂) be an unbounded and increasing sequence of real numbers. Prove that x (x₂) diverges to + ∞0.

Q: dx Evaluate f- +1) using the Cauchy principal value.

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Q: Prove for a > 0:

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Q: Let f(x) = 6x² + 2x³. Select all intervals where f(x) is INCREASING, (3) (0, ∞) (,0) (-∞, -3¹²¹)

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Q: Find a number x such that x + 1 / x − 2 = 3x

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Q: A -5 < x < -4.5 0.5 < x <1 1.5 < æ < 2.5 D None of the above

A: Given a graph of function h(x).

Q: Find the interval in which the function f(x) = (x +9)4 + 6 is increasing. (Use symbolic notation and…

A: The objective of this question is to find the interval in which the function f(x) = (x + 9)^4 + 6 is…

Q: (c) A non-constant function f : [0, 1] → R such that f(x) > 0 for any r e [0, 1] but | f(x)dx = 0.…

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Q: Soec "x dx X,

A: If we have integral  ∫f(x).g(x) = f(x)∫g(x)dx  - ∫f'(x)∫g(x) dx where ,f(x) is first function and…

Q: Let C be a fixed positive constant. If {bn} is a sequence of nonnegative numbers such that lim (as…

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Q: PROVE THAT Q(-∞) =1 usign Q – Function

A: Given that Q-∞=1

Q: (c) A non-constant function f : [0, 1] → R such that f(x) > 0 for any x e [0, 1]I f(x)dx = 0. Give a…

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Q: Which function grows faster as O x → +∞ ? 3x¹ + 2x³ + 3x² +1 x³ ln(x² + 1)

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Q: Find the value of: 2 100 ;] [*] + x + 100 ] + [~ + + ++ 99 100

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Q: Let f(n) and g(n) be functions satisfying  f(n) = {sqrt (n), 1 + f(n+1)} if sqrt (n) is an integer…

A: Let f(n)={n,1+f(n+1)} To find 1+f(n+1) replace n by n+1 in f(n) therefore, f(n+1)=n+1 and…

Q: find the positive intervals for  x2 − 3x

A: We need to find the interval for which function is positive .

Q: "hich of the following statements is true of f(x)= -x³-6x²-9x-2? A. fis increasing on (-3,-1) B. fis…

A: We will find the required.

Q: Let f(x)=(x-4)/(x+8). Find the open intervals on which f is increasing

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