Let fn(x) on [0, 1]. 1+ nx (a) Does fn converge uniformly on [0, 1]? (b) Check if lim | fn(x) dæ lim fn(x) dx. n00 n00

Q: Let f(x) = 1²-16 +4 1²-16 H-4 x > 0 I≤0 Find lim f(1)

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Q: (2x – x? if 0 sxS2 if 0 sxs2 2 -x if 2 < x<3 x - 2 if 3 <x < 4 if x 24 f(x) =

A: We have to find

Q: Vx + 2 – 2 Evaluate the limit lim x→2 x2 – 4

A: We can evaluate the limit in the following steps.

Q: Select all that apply: ☐ f(x) is defined at x = −3. Olim f(x) exists. x-3 ☐_lim f(x) = f(−3). x→-3…

A: To determine the correct choices.

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Q: Determine whether f(x) = approaches o or - as x approaches - 5 from the left and from the x² - 25…

A: Given that f(x) = x8 / (x2 - 25) = x8 / (x + 5)(x - 5) . Other than x = +5, -5 f(x) is defined…

Q: 1. The average rate of change of f(x) = (x − 1)(x + 2) over the interval -1 ≤ x ≤ 1 is a. -2 b. 1 C.…

A: To find the average of change of  over the interval .Note: Since you have posted multiple questions,…

Q: 3. Using limit, compare the order of the growth of functions. a) n4 & 2n b) log₂n & n c) n³ & log2n…

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Q: V9x4 + 2 sin x Evaluate lim x→+∞ Зx2 — 5 03 O 1 3 O 1 None of these or the limit does not exist

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Q: limx→o (t+1)f(t)dt Assume f (0) = 4 %3D 3x2

A: Explanation of the answer is as follows

Q: The limit represents f '(c) for a function f(x) and a number c. Find f(x) and c. [7-9(4+ Ax)]- (-29)…

A: lim∆x→07-94+∆x--29∆x The derivative of a function f(x) at the point x = c is, lim∆x→0fc+∆x-fc∆x

Q: Find lim f(x) if, for all x > 1, x → 00 4 12ex - 24 4ex X 3√x √x-1

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Q: Find lim f (x) where 2 f (x) = 1 In x a. infinity O b. negative infinity С. О d. 1

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Q: 3. For each part, sketch a function f that satisfies all the conditions, if possible. If not…

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Q: ff is continuous and ƒ(5) = 2 and ƒ(4) = 3 then lim ƒ(4x² — 11) = 2. x→2 True False

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Q: Let f be a continuous function with domain R. Assume fis POSITIVE and DECREASING. Assume lim f(z) =…

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Q: The graph below is the function f(x) 5+ 4 3 2 01 -5 -4 -3 -2 -1 -1 -2 3 -4 -5+ 1 2 4 5 Determine…

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Q: If f(x) = 2x? – x + 2 , what is lim 2x2 – x + 2, lim 2x2 – x + 2, andf(2)? Is f(x)continuous at 2? O…

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