Consider the function below. Use it to evaluate each of the following expressions. (If an expression does not exist, enter NONE.) if x < 1 if x = 1 if 1 < x≤ 2 if x > 2 g(x) = = x 9 2-² x - (a) lim g(x) z 1- (d) lim g(x) x 2 (b) lim g(x) z+1+ (e) lim g(x) z→2+ (c) g (1) (f) lim g (x) x 2

Q: If lim I+- 00 f(x) f(x) also equals -2. 2 with f(x) and g(x) both polynomials then lim g(x) I- 00…

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Q: 11. If f(x)=Vx f(x)-f(4)| The lim x→4 х-4

A: Given: fx=x To Find:  limx→4fx-f4x-4=?

Q: Evaluate

A: To evaluate limx→0 e2x-1xSubstituting x=0 , 00 form is obtained Hence , L' Hospital's rule can be…

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A: We have to evaluate the limit: limx→∞xe-x Rearranging the question using exponent rule a-m=1am,…

Q: 2x+12 |x+6| If f(x)=- , determine whether lim f(x) exists. 44-6

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Q: If 3x < f(x) < x³ + 2 for 0 < x < 2, find lim f(x). x-1

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

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Q: If lim fx) -6 х+1 х— 1 – 6 10 , evaluate lim f(x).

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Q: if f(2) = 4 f (2) = 1 Then Xf (2)-2г (x) lim x→2 X-2

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Q: Determine the right- and left-sided limits of the following function: lim x-3- (x + 1) lim x-3+x - 3

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Q: 2 lim_x(x²) +0+x

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Q: f(7+h) – f(7) lim h>0 h here f(x) = 7r +4. If the limit does not exist enter DNE.

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Q: If lim fx) - 7 x-1 x - 1 5, evaluate lim f(x). X-1

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Q: Evaluate  lim

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Q: If -a2 + 6x – 7 < f(x) < 2x – 3 for all r, find lim f(x). Cite any relevant theorems used.

A: Given that,  -x2+6x-7≤fx≤2x-3 To determine limx→2fx. By the algebra of limits, If gx≤hx  then…