Chapter 2: Q. 2 (page 164)

Approximating limits: Use sequences of approximations to estimate the values of
$\lim_{x \to 2} \frac{4 - x^{2}}{2 - x} \lim_{z \to 3} \frac{z^{3} - 27}{z - 3}$

Short Answer

Expert verified

Limits values are following.

$\lim_{x \to 2} \frac{4 - x^{2}}{2 - x} = 4 \lim_{z \to 3} \frac{z^{3} - 27}{z - 3} = 27$

Step by step solution

Step 1. Given information.

Given limits are the following.

$f (x) = \lim_{x \to 2} \frac{4 - x^{2}}{2 - x} f (x) = \lim_{z \to 3} \frac{z^{3} - 27}{z - 3}$

Step 2. Limit value of limx→24-x22-x

Find the Limit value $\lim_{x \to 2} \frac{4 - x^{2}}{2 - x} .$

$\lim_{x \to 2} \frac{4 - x^{2}}{2 - x} = \lim_{x \to 2} \frac{2^{2} - x^{2}}{2 - x} = \lim_{x \to 2} \frac{(2 - x) (2 + x)}{2 - x} = \lim_{x \to 2} (x + 2) = 2 + 2 = 4$

So the value of $\lim_{x \to 2} \frac{4 - x^{2}}{2 - x}$ is $4 .$

Step 3. Limit value of limz→3z3-27z-3

Determine the limit value $\lim_{z \to 3} \frac{z^{3} - 27}{z - 3} .$

localid="1649805298120" $\lim_{z \to 3} \frac{z^{3} - 27}{z - 3} = \lim_{z \to 3} \frac{z^{3} - 3^{3}}{z - 3} = \lim_{z \to 3} \frac{(z - 3) (z^{2} + 3 x + 3^{2})}{z - 3} = \lim_{z \to 3} (z^{2} + 3 x + 9) = 3^{2} + 3 (3) + 9 = 27$

So the value of $\lim_{z \to 3} \frac{z^{3} - 27}{z - 3}$ is $27 .$

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Approximating limits: Use sequences of approximations to estimate the values of
$\lim_{x \to 2} \frac{4 - x^{2}}{2 - x} \lim_{z \to 3} \frac{z^{3} - 27}{z - 3}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Limit value of limx→24-x22-x

Step 3. Limit value of limz→3z3-27z-3

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Approximating limits: Use sequences of approximations to estimate the values oflimx→24-x22-xlimz→3z3-27z-3

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Limit value of limx→24-x22-x

Step 3. Limit value of limz→3z3-27z-3

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Approximating limits: Use sequences of approximations to estimate the values of
$\lim_{x \to 2} \frac{4 - x^{2}}{2 - x} \lim_{z \to 3} \frac{z^{3} - 27}{z - 3}$