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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2, Problem 1RE

**(a)**

To determine

**To find:** The limit of each of the given functions and explain if the limit does not exist.

Expert Solution

(i) The value of

(ii) The value of

(iii) The value of

(iv) The value of

(v) The value of

(vi) The value of

(vii) The value of

(viii) The value of

**Calculation:**

**Section (i)**

Obtain the value of

From the given graph, it is found that the curve move towards *x* approaches 2 from the right, that is

Therefore,

**Section (ii)**

Obtain the value of

From the given graph, it is found that the curve move towards *x* approaches

Therefore,

**Section (iii)**

Obtain the value of

From section (ii),

From the given graph, it is found that the curve move towards *x* approaches

Thus,

Recall the definition that

Since

Therefore,

**Section (iv)**

Obtain the value of

From the given graph, it is found that the curve move towards *x* approaches

Therefore,

**Section (v)**

Obtain the value of

From the given graph, it is found that the curve move towards infinity as *x* approaches

Therefore,

**Section (vi)**

Obtain the value of

From the given graph, it is found that the curve move towards negative infinity as *x* approaches 2 from the left side.

Therefore,

**Section (vii)**

Obtain the value of

From the given graph, it is found that the curve move towards *x* approaches infinity.

Therefore,

**Section (viii)**

Obtain the value of

From the given graph, it is found that the curve move towards *x* approaches negative infinity.

Therefore,

**(b)**

To determine

**To state:** The equation of horizontal asymptotes.

Expert Solution

The equation of horizontal asymptotes are

Recall from the definition that

From the previous parts,

Thus, equation of horizontal asymptotes are

**(c)**

To determine

**To state:** The equation of vertical asymptotes.

Expert Solution

The equation of vertical asymptotes are

Recall from the definition that

From the previous parts,

Thus, equation of vertical asymptotes are

**(d)**

To determine

**To find:** The numbers at which *f* is discontinuous.

Expert Solution

*f* is discontinuous at

From the given graph,

Thus, *f* is discontinuous at

From the given graph,

Thus, *f* is discontinuous at

From the given graph,

Thus, *f* is discontinuous at

From the given graph,

Recall from the definition that *f* is continuous at

Thus, *f* is discontinuous at

Therefore, *f* is discontinuous at