Chapter 1: Q. 6 (page 97)

Find punctured intervals on which the function $f (x) = \frac{1}{x \ln (x + 2)}$ is defined, centered around
$(a) x = 0 (b) x = - 1 (c) x = - 1.5$

Short Answer

Expert verified

Part (a). The punctured intervals is $(- 0.5, 1) \cup (0, 0.5)$ .

Part (b). The punctured intervals is $(- 1.5, - 1) \cup (- 1, - 0.5)$ .

Part (c). The punctured intervals is $(- 2, - 1.5) \cup (- 1.5, - 1)$ .

Step by step solution

Step 1. Given information.

The given function is $f (x) = \frac{1}{x \ln (x + 2)}$ .

Part (a) Step 1. Calculation.

For $x = 0$

The punctured interval $(c - δ, c) \cup (c, c + δ)$ is given by:
$(0 - 0.5, 0) \cup (0, 0 + 0.5) = (- 0.5, 1) \cup (0, 0.5)$

Part (b) Step 1. Calculation.

For $x = - 1$

The punctured interval $(c - δ, c) \cup (c, c + δ)$ is given by:

$(- 1 - 0.5, - 1) \cup (- 1, - 1 + 0.5) = (- 1.5, - 1) \cup (- 1, - 0.5)$

Part (c) Step 1. Calculation.

For $x = - 1.5$

The punctured interval $(c - δ, c) \cup (c, c + δ)$ is given by:
$(- 1.5 - 0.5, - 1.5) \cup (- 1.5, - 1.5 + 0.5) = (- 2, - 1.5) \cup (- 1.5, - 1)$

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Find punctured intervals on which the function $f (x) = \frac{1}{x \ln (x + 2)}$ is defined, centered around
$(a) x = 0 (b) x = - 1 (c) x = - 1.5$

Short Answer

Step by step solution

Step 1. Given information.

Part (a) Step 1. Calculation.

Part (b) Step 1. Calculation.

Part (c) Step 1. Calculation.

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Find punctured intervals on which the function fx=1xlnx+2is defined, centered around ax=0bx=-1cx=-1.5

Short Answer

Step by step solution

Step 1. Given information.

Part (a) Step 1. Calculation.

Part (b) Step 1. Calculation.

Part (c) Step 1. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

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Find punctured intervals on which the function $f (x) = \frac{1}{x \ln (x + 2)}$ is defined, centered around
$(a) x = 0 (b) x = - 1 (c) x = - 1.5$