Let X if x < 1 5 if x = 1 g(x) 2 x2 if 1 2 (a) Evaluate each of the following, if it exists. (If an answer does not exist, enter DNE.) (i) lim g(x) x 1 (ii) lim g(x) x+1+ (iii) g(1) (iv) lim g(x) x-2 (v) lim g(x) x-2+ (vi) lim g(x) x-2 (b) Sketch the graph of g. 2x

Q: If f(x) is defined by the following ²-16 =x2-4 2-3x-1 Let f(x) x> 2 *<2 Then find the lim f(x) & lim…

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Q: Find lim f(x) if, for all x > 1, x- 00 6ex - 15 < f(x) < 3ex Vx - 1 х —

A: 6ex-153ex&lt;f(x)&lt;2xx-1

Q: Example 2. Prove that lim f(r) =1 by use of Definition 3, where f is given by - 21 +2 if a 2 f(x) =…

A: Given the proof of limx→2fx=1, where fx=x2-2x+22if x≠22if x=2 Here equation (c) is, fx-1≤32x-2 Also,…

Q: x – 1 is X +2 The rang of f(x)= y = ,

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Q: 4х — 1 4x2 + 3x Find lim f(x) if 5. x2

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Q: d. lim x_1 x-1

A: Since there are multiple questions so according to guidelines we can solve only first one.

Q: 11) Evaluate lim (1+ 2x)csc(x).

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Q: Let g(x) and h(X) be functions with lim g (x) = G and lim h (x) = Hwhere G and H are real numbers.…

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Q: (g) lim (x- Vx +x - Vx-x (h) lim 3x²

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Q: 4х — 1 4x2 + 3x - Find lim f(x) if 5. x2

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Q: if x1 then lim,-1 f(x) is 3 if x 1 (b) 3 3. Let f(x) = (a) 1 (c) not exist (d) other

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Q: True or false: If lim f(x) = f(a), and x1 is closer to a than x2, then f(x1) is closer to f(a) x→a…

A: The given statements is: If limx→af(x)=f(a)  and x1 is closer to a than x2 then fx1 is closer to…

Q: If lim x→0 a) f(x) x = 1 and lim x-0 lim g(x) x→0 g(x) – 2, evaluate: X b) lim x-0 g(x) f(x)

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Evaluate V1+ sin x V1+ tan x lim x→0 - x3

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Q: x²-1 if x < -1 -2 if x ≥ - 1 lim g(x), where g(x) = x+1 x-

A: Steps:

Q: a. lim f(x) X-4

A: