$$\lim_{x \to a} [f(x) - g(x)] = \lim_{x \to a} f(x) \cdot \lim_{x \to a} g(x)$$

Question 1

Which of the following is a valid application of the limit laws for evaluating $$\lim_{x 	o 2} (3x^2$ + 5x)$$?

Accepted Answer

Apply the sum, constant multiple, and power laws to evaluate the limit by direct substitution.

Question 2

Evaluate $$\lim_{x 	o -2} (x^2$ + 5x + 7).$$

Accepted Answer

$$1$$

Question 3

Which technique is most appropriate for evaluating $$\lim_{h 	o 0} \frac{\sqrt{16 + h} - 4}{h}$$?

Accepted Answer

Multiply numerator and denominator by the conjugate of the numerator.

Question 4

Evaluate $$\lim_{x 	o 1} \frac{f(x)}{h(x)}$$ given $$\lim_{x 	o 1} f(x) = 8$$ and $$\lim_{x 	o 1} h(x) = 2.$$

Accepted Answer

$$4$$

Question 5

A pharmaceutical company models the concentration of a drug in the bloodstream as $$C(t) = 4t^2$ - 7t + 2. $$What is $$\lim_{t 	o 2} C(t)$$?

Accepted Answer

$$6$$

Question 6

Evaluate $$\lim_{x 	o b} \frac{(x-b$$)^{50}$$ - x + b}{x-b}$$ for a fixed real number $$b.$$

Accepted Answer

$$-1$$

Question 7

Which of the following statements is TRUE about $$\lim_{x 	o -6} 4$$?

Accepted Answer

The limit is $$4$$ because the limit of a constant function is always the constant.

Question 8

Evaluate $$\lim_{p 	o 2} \frac{3p}{\sqrt{4p + 1} - 1}.$$

Accepted Answer

$$3$$

Question 9

A biologist is studying the population growth modeled by $$P(t) = (3t-1)(t-2). $$What is $$\lim_{t 	o 2} P(t)$$?

Accepted Answer

$$-5$$

Question 10

Evaluate $$\lim_{t 	o 5} \left( \frac{1}{t-5} - \frac{1}{t+1} ight).$$

Accepted Answer

$$-\frac{1}{36}$$

Question 11

Evaluate $$\lim_{x 	o 0} \frac{1 - \cos 2x}{\sin x}$$ using trigonometric identities.

Accepted Answer

$$0$$

Question 12

Given $$f(x) = \begin{cases} x^2$ + 1 & x \u003c -1 \ \sqrt{x+1} & x \geq -1 \end{cases}$$, what is $$\lim_{x 	o -1^-} f(x)$$?

Accepted Answer

$$2$$

Question 13

Given $$f(x) = \begin{cases} x^2$ + 1 & x \u003c -1 \ \sqrt{x+1} & x \geq -1 \end{cases}$$, what is $$\lim_{x 	o -1^+} f(x)$$?

Accepted Answer

$$0$$

Question 14

Given $$f(x) = \begin{cases} x^2$ + 1 & x \u003c -1 \ \sqrt{x+1} & x \geq -1 \end{cases}$$, what is $$\lim_{x 	o -1} f(x)$$?

Accepted Answer

Does not exist

Question 15

Which of the following is NOT a valid limit law?

Accepted Answer

$$\lim_{x 	o a} [f(x) - g(x)] = \lim_{x 	o a} f(x) \cdot \lim_{x 	o a} g(x)$$

Techniques for Computing Limits

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