Question 1

If the left and right limits at x = 4 are different, what can you conclude?

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Question 2

If lim_(x→2) f(x)=7, which statement is true?

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Question 3

Evaluate lim_(x→5)(3x-4).

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Question 4

Evaluate lim_(x→3)(x^2-9)/(x-3).

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Question 5

If lim_(x→1^-)f(x)=2 and lim_(x→1^+)f(x)=2, then lim_(x→1)f(x) =

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Question 6

Evaluate lim_(x→2)(x^2+3x-1).

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Question 7

Evaluate lim_(x→4)(x^2-16)/(x-4).

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Question 8

A table shows f(x) → 7 as x → 2 from both side. Estimate lim_(x→2)f(x) and state what the table tells you about f(2).

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Question 9

For f(x) = (x² − 1)/(x − 1):

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Question 10

A piecewise function has both one-sided limits equal to 4 at x=a, but f(a)=-3. Determine lim_(x→ a)f(x) and comment on continuity.

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Question 11

Given lim_(x→3^-)f(x)=5 and lim_(x→3^+)f(x)=7, explain whether lim_(x→3)f(x) exist.

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Question 12

A graph approaches y=2 as x approaches 1 from both side, but f(1)=10. Find lim_(x→1)f(x).

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Question 13

Evaluate lim_(x→0)((x+1)^2-1)(x).

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Question 14

A population model gives P(t)=(t^2-25)/(t-5). Use limits to find the rate indicator at t=5 and interpret your answer.

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Question 15

For g(x)=(|x|)/(x), find both one-sided limits at x=0 and state whether the two-sided limit exist.

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Topic 5.1: Introduction to Differentiation Questions

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