Let fn(x) n²x²(1 – x) on [0, 1]. Let e > 0. Does lim,0 m ({x € [0, 1]|fn(x) > e}) exist?

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A: Note the result: If uniformly, is true. If point wise, can be true or false.

Q: in z2 Q5. Find the value of the limit: lim in z²+1 .- 기 z→e 2

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A: Given limn→∞∑j=1n1/j2-∫1πdxx2

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A: To find: The value of limit limx→+∞e3x+ln xe2x+x2. Concept used: Properties of limit:…

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A: Here we need to construct a bounded sequence {λn}  , which is bounded.

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A: we have find the value of limx→0ex-e-xsin x

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Q: 1. Find the limit of the following functions: x2/3+x-1 lim e x2/3 + cos² x 1- cosx lim- -+0 sin2x

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Q: Express the limit lim n→∞ a = n b = i=1 Provide a, b and f(x) in the expression (6 cos² (2πx)+5) Ax;…

A: To find value of a, b and f(x).

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Q: 4. Evaluate the limit of as e approaches 0. 2a A 2 B. % CO D. infinity

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Q: Exercise 6. Find the limits. 1 dx. 1+ x2n lim

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Q: Let fn(x) = n²x²(1 – x) on [0, 1]. Does lim,oo fn(x) exist for every r E [0, 1]?

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Q: OF# Usc the L'Hospital's Rule to compute the limits: B) lim x+5 B00 2x+5* A) lim log, (1+ 2x+x?) and…

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Q: Let fn(x) = n²x²(1 – x) on [0, 1]. Does lim,-00 So fn(x) exist?

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A: First, we will find the general Taylor series of f(x) = tan x centered at x = π/3. We know that…

Q: - Evaluate the limit a-Lim(x/(x-1) – 1/ Inx) b- lim [In(cos(x)) c-2-VX-+4 /sin'x x>1 x>0 d- lim x+1…

A: Limit values

Q: Evaluate the limit lim Eƒ(ci)Ax¡ over the region bounded by 3%3D1 n-00 the graphs of the equation f…

A: To: Evaluate the limit limn→∞∑i=1nf(ci)∆xi over the region bounded by the graphs of the equation…

Q: Suppose that functions g(t) and h(t) are defined for all values of t and g(0) = h(0) = 0. Can…

A: Given that functions g(t) and h(t) are defined for all values of t and g (0) = h (0) = 0.

Q: Let an for all n e N. Working directly from the Vn+1 definition show that limn- An = 1.

A: To evaluate limn→∞ nn+1: Here, an=nn+1 an can also be written as: an=1n+1n Simplifying this we get,…

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Q: Evalvate the limit lim Cos x In(x- TT Xーつク nピ-e)

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Q: 2. Let x E (0, 1), use e – d to prove V4 +x – 2 lim 1 4

A: 2. Given x∈0,1, limx→04+x-2x=14                       ... (1) Use ε-δ definition to prove above the…

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A: Given,          fx=-4+2x4-6x

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Q: find the limit as x goes to infinity of ln(x+1/x+2)

A: Evaluate the limit

Q: Consider g(x)=−7x3+7x2+9. a) limx→0−g(x)= b)limx→−1−g(x)= c)On what interval(s) is g(x)…

A: It can be solved using the limiting definition of continuity

Q: Given that f,(x) = (n+ 1)(n+ 2)(1 – x)x" and that f(x)= 0 for × €[0,1] 1. Show that the limit lim…

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Q: (b) Use the sandwich theorem to show that limy0x°cos - = 0. 1 In order to apply the sandwich…

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Q: 1-e X x2 +1 X By using the limit comparison test, the integral

A: Using, limit comparison test

Q: 1. Show that for all f e L'(R) lim da = 0.

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A: We find out limit of given function. See 2nd step.

Q: Prove that lim n 00 a" f (x) dx = 0, for any f E R[0, 1].

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