Consider the sequence of functions {fn}=2 where fn: [a, b] → R defined for n 2 2 by if 0

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Q: Suppose X~N(196,20). Find x such that Pr(X > x) = 0.619.

A: The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ are the mean…

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Q: Start with an initial guess x = a₁. Then define a2 to be the x-intercept of the tangent of f(x) at…

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Q: Suppose f(x) is continuous on [3, 8] and -5 < f'(x) < 3 for all x in (3, 8). Use the Mean Value…

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Q: It is known that function f is an increasing function that satisfies f(-1) = 4 and f'(-1) = 2. Use…

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Q: Let F(t) = (4t³ - 1)j + (5t+2)k. Find F'(t). 7"(t) O 288t 288t³j 05+288t³ O 36t³ +5 O None of these

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Q: Give an example of a sequence of differentiable functions {f_n: (-1,1)—>R} that converges uniformly…

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Q: Does sin () x 7 converge or diverge? Why?

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Q: The sketch that represents a continuous function, y = f(x), such that: f'(-3)=Ø f(-3) = 5 and A(1) =…

A: The graph of continuous function f(x) is given in the options. The given data of the function f(x)…

Q: 52. f(æ) = (-1)**(x – 2)". %3D n=1

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Q: On what open interval is  f '  an increasing function?   For which value of x is  f '(x)  minimum?

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Q: The graph of f is shown in the figure. 6. 4 х 14 -4 -6+ 2-

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Q: Use the MVT to prove that if f' (x) ≤ 2 for x &gt; 0 and f (0) = 4, then f (x) ≤ 2x + 4 for all x ≥…

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Q: Use the given graph of f(x) to find the intervals on which f'(x) > 0. 20+ 15 10 5+ -7 6 -5 3 2 -1…

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Q: Find the arc length (s) of the curve 7(t) = (e*, 4e", - 2et) for 0 <t < In(5) |

A: we are given the curve  r→(t)=e5t,-4e5t,-2e5t =e5ti-4e5tj-2e5tkwhere 0≤t≤ln5

Q: Let 7(t) = Find 7'(t) F'(t) =

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Q: Let ∫∞−∞ f(x) dx be convergent and let a and b be real numbers where a ≠ b. Show that

A: Let ∫-∞∞f(x)dx is convergent and a,b∈-∞,∞ To Show: ∫-∞af(x)dx+∫a∞f(x)dx=∫-∞bf(x)dx+∫c∞f(x)dx     If…

Q: The number of new prison admissions (into state or federal facilities) between 2002 and 2011 is…

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Q: X° +4x dx x* +3x² +2 4 2 1

A: Topic :- Integration If the limit exists as a real number, then the simple improper integral is…

Q: Let fn(x) = x^n for x ∈ [0,1]. check if it is pointwise convergence. Define where it becomes…

A: Given, fn(x) = xn , x ∈ [0,1].We will check poitwise convergence of fn on [0,1].