Chapter 1: Q. 66 (page 88)

Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 53–66. If a two-sided limit does not exist, describe the one-sided limits.
$\lim_{x \to - 1} f (x), f o r f (x) = \{\begin{cases} x + 1, i f x < - 1 \\ 2, i f x = - 1 \\ - x^{2}, i f x > - 1 \end{cases}$

Short Answer

Expert verified

The graph of the given limit

The limit expression has the value of $\lim_{x \to - 1} f (x) = 2$

Step by step solution

Step 1. Given information

The given limit $\lim_{x \to - 1} f (x), f o r f (x) = \{\begin{cases} x + 1, i f x < - 1 \\ 2, i f x = - 1 \\ - x^{2}, i f x > - 1 \end{cases}$

Step 2. Sketch graphs by hand and use them to make approximations for the limit

The graph is drawn as below:

From the graph,we see that for the left of $x \to - 1$ the value of the function is 0. Again for the right of $x \to - 1$ the value is -1.But it has the value of 2 at $x = - 1$

Therefore,the limit expression has the value of $\lim_{x \to - 1} f (x) = 2$

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Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 53–66. If a two-sided limit does not exist, describe the one-sided limits.
$\lim_{x \to - 1} f (x), f o r f (x) = \{\begin{cases} x + 1, i f x < - 1 \\ 2, i f x = - 1 \\ - x^{2}, i f x > - 1 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Sketch graphs by hand and use them to make approximations for the limit

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Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 53–66. If a two-sided limit does not exist, describe the one-sided limits.limx→-1f(x),forf(x)=x+1,ifx<-12,ifx=-1-x2,ifx>-1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Sketch graphs by hand and use them to make approximations for the limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Decision Maths

Theoretical and Mathematical Physics

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 53–66. If a two-sided limit does not exist, describe the one-sided limits.
$\lim_{x \to - 1} f (x), f o r f (x) = \{\begin{cases} x + 1, i f x < - 1 \\ 2, i f x = - 1 \\ - x^{2}, i f x > - 1 \end{cases}$