Consider f: (0, 2)→ R defined by f(x)=x". Assume that f has a limit at 0 and find that limit. (Hint: Choose a sequence (x)-1 converging to 0 such that the limit of the sequence (f(x)} is easy to determine.)

Q: 3. Let f : R - {0} → R be such that the sequence (xnf (xn)) converges to 3 whenever (xn) is a…

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Q: 2. Use the ɛ-d definition of the limit of a function to prove that lim = 3. I-»3 T – 2

A: Let  I  be an open interval containing  c , and let  f  be a function defined on  I , except…

Q: (-x² +5 if x<-1 Let p(x)={ax² +b if -1<x<3. Use the limit definition of continuity to help you (a.)…

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Q: S* 56sin(t")dt Evaluate the limit lim .8

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Q: Consider the function G: R²\{0} → R defined by 12,8 (x10 + x10)² G(x): = Find an expression for the…

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Q: lim t→∞ 14/3 + 71/3 2 (6+²/3 +11) ²

A: To find out the limit.

Q: Which of the following is the limit of f(x)= 1-5x as x appro qchers 1 a. - 2 d. does not exist

A: If the denominator and numerator gives a non zero value on applying the value where limit to be…

Q: (e) limVx ) lim -+(-1)") X-00 n→0 n n²-12345 x2 +9 (g) lim n +1 (h) lim x∞x3 +1

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Q: 23) lim f(x) x→1- f(x) 5- 4+ 3+ 2+ -5 -4 -3 -2 -1 -1. 5 х 2 4 -2+ -3+ -4+

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Q: 4) Make a table for a sequence of carefully chosen values of a to estimate the limit 1® – 1 f(x) =…

A: By using table value of x for this given function to estimate this given limit

Q: Evaluate sin 0 – 1 lim 0 - T/2 In sin 0

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Q: Compute the limit lim Ssin n2 .1+n2 (규)]. n00

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Q: Find the limit

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Q: х2—1 lim х-1+ In(x)

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Q: Evaluate the limit lim 6 (²1) y→2_8y²(y − 1)³

A: To evaluate the following limit. limy→2 6y2-18y2y-13

Q: In(9x) (d) lim x2

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Q: Evaluate the limit using the identity a³ — b³ = (a − b)(a² + ab + b²): lim x³-512 x-8 x→8

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Q: Compute the limit if it exists, otherwise show your reason why the limit does not exist. |22 – r|…

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Q: EVALUATE THE LIMIT OF THE GIVEN FUNCTIONS

A: The value of 1/infinity is 0. So using this knowledge we got into this problem.

Q: (b) lim (r + 1) In x

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Q: 3. Let f : R- {0} → R be such that the sequence (xnf(xn)) converges to 3 whenever (n) is a sequence…

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Q: 2x2 -7х — 4 9) lim х-4 х2 — х — 12

A: From the given problem: limx→ 42x2-7x-4x2-x-12 So, we can simply write as: limx→…