Q: Which of the following statements is true about $$g(x) = \dfrac{|x-2|}{x-2} as$$ $$x$$ approaches 2 from the right?

$$\lim\limits_{x \to 2^+} g(x) = 1$$

Q: Which of the following is the correct definition of a one-sided limit from the left?

$$\lim\limits_{x \to a^-} f(x) = L if$$ $$f(x)$$ approaches $$L as$$ $$x$$ approaches $$a$$ from values less than $$a.$$

Q: Suppose $$f(x)$$ increases without bound as $$x$$ approaches $$a$$ from the left. Which of the following is correct?

$$\lim\limits_{x \to a^-} f(x) = +\infty$$

Q: If $$f(x)$$ decreases without bound as $$x$$ approaches $$a$$ from the right, which of the following is correct?

$$\lim\limits_{x \to a^+} f(x) = -\infty$$

Q: Which of the following best describes an infinite limit from the right?

$$\lim\limits_{x \to a^+} f(x) = +\infty if$$ $$f(x)$$ increases without bound as $$x$$ approaches $$a$$ from the right.

Question 1

Which of the following best defines the two-sided limit $$\lim\limits_{x 	o a} f(x) = L$$?

Accepted Answer

The value of $$f(x)$$ approaches $$L as$$ $$x$$ approaches $$a$$ from both the left and the right.

Question 2

Evaluate $$\lim\limits_{x 	o 2} \dfrac{x^2$ - 4}{x - 2}.$$

Accepted Answer

2

Question 3

Which of the following statements is true about $$g(x) = \dfrac{|x-2|}{x-2} as$$ $$x$$ approaches 2 from the right?

Accepted Answer

$$\lim\limits_{x 	o 2^+} g(x) = 1$$

Question 4

Evaluate $$\lim\limits_{x 	o 3^-} \dfrac{|x^2$ - 9|}{x - 3}.$$

Accepted Answer

-6

Question 5

Which of the following is the correct definition of a one-sided limit from the left?

Accepted Answer

$$\lim\limits_{x 	o a^-} f(x) = L if$$ $$f(x)$$ approaches $$L as$$ $$x$$ approaches $$a$$ from values less than $$a.$$

Question 6

Suppose $$f(x)$$ increases without bound as $$x$$ approaches $$a$$ from the left. Which of the following is correct?

Accepted Answer

$$\lim\limits_{x 	o a^-} f(x) = +\infty$$

Question 7

Evaluate $$\lim\limits_{x 	o 2^+} \dfrac{|x-2|}{x-2}.$$

Accepted Answer

1

Question 8

Evaluate $$\lim\limits_{x 	o 2^-} \dfrac{|x-2|}{x-2}.$$

Accepted Answer

-1

Question 9

Which of the following is true about the existence of $$\lim\limits_{x 	o a} f(x)$$?

Accepted Answer

The two one-sided limits must both exist and be equal.

Question 10

A chemical reaction rate $$R(t) is $$modeled by $$R(t) = \dfrac{t^2$ - 16}{t - 4}. $$What is $$\lim\limits_{t 	o 4} R(t)$$?

Accepted Answer

8

Question 11

If $$f(x)$$ decreases without bound as $$x$$ approaches $$a$$ from the right, which of the following is correct?

Accepted Answer

$$\lim\limits_{x 	o a^+} f(x) = -\infty$$

Question 12

Evaluate $$\lim\limits_{x 	o 3^+} \dfrac{|x^2$ - 9|}{x - 3}.$$

Accepted Answer

6

Question 13

A patient’s medication concentration $$C(t) is $$given by $$C(t) = \dfrac{|t-5|}{t-5}. $$What is $$\lim\limits_{t 	o 5^-} C(t)$$?

Accepted Answer

-1

Question 14

Which of the following is NOT a requirement for $$\lim\limits_{x 	o a} f(x) = L to $$exist?

Accepted Answer

The function must be defined at $$x = a.$$

Question 15

Suppose $$f(x) is $$defined as $$f(x) = \dfrac{x^2$ - 1}{x - 1}. $$What is $$\lim\limits_{x 	o 1} f(x)$$?

Accepted Answer

2

Question 16

If $$\lim\limits_{x 	o a^-} f(x) = 3$$ and $$\lim\limits_{x 	o a^+} f(x) = 5$$, what can you conclude about $$\lim\limits_{x 	o a} f(x)$$?

Accepted Answer

The limit does not exist.

Question 17

A function $$h(x) is $$such that $$\lim\limits_{x 	o 0^-} h(x) = +\infty$$ and $$\lim\limits_{x 	o 0^+} h(x) = -\infty. $$What is $$\lim\limits_{x 	o 0} h(x)$$?

Accepted Answer

Does not exist

Question 18

Which of the following best describes an infinite limit from the right?

Accepted Answer

$$\lim\limits_{x 	o a^+} f(x) = +\infty if$$ $$f(x)$$ increases without bound as $$x$$ approaches $$a$$ from the right.

Question 19

A function $$f(x) is $$defined as $$f(x) = \dfrac{|x-1|}{x-1}. $$What is $$\lim\limits_{x 	o 1} f(x)$$?

Accepted Answer

Does not exist

Limits and One-Sided Limits in Calculus

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