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Chapter 1: Q. 38 (page 88)

Consider the graph of the function:

Find the limits of function.

Short Answer

Expert verified

The values of the given limits are 1.75,0,-2,∞.

Step by step solution

01

Step 1. Given graph

02

Step 2. Finding limits at point x=0

Herethelimitexpressionislimx->0g(x)Fromthegraph,thefunctionalvaluetowardsx=0isg(x)=1.75Therefore,limx->0g(x)=1.75

03

Step 3. Finding limits at point x=3

Herethelimitexpressionislimx->3g(x)Fromthegraph,thefunctionalvaluetowardsx=3isg(x)=0Therefore,limx->3g(x)=0

04

Step 4. Finding limits at point x= -∞

Herethelimitexpressionislimx->-∞g(x)Fromthegraph,thefunctionalvaluetowardsx=-∞isg(x)=-2Therefore,limx->-∞g(x)=-2

05

Step 5. Finding limits at point x= ∞

Herethelimitexpressionislimx->∞g(x)Fromthegraph,thefunctionalvaluetowardsx=∞isg(x)=∞Therefore,limx->∞g(x)=∞

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Most popular questions from this chapter

For each limit statement , use algebra to find δ > 0 in terms of ε> 0 so that if 0 < |x − c| < δ, then | f(x) − L| < ε.

limx→12x4=2;youmayassumeδ≤1.

Calculate each of the limits:

limx→3xtan-1x

Write delta-epsilon proofs for each of the limit statements limx→cfx=Lin Exercises 47-60.

limx→-31-x=4.

Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Extreme Value Theorem, and illustrate on your graph that the conclusion of the Extreme Value Theorem does not necessarily hold.

State what it means for a function f to be left continuous at a point x = c, in terms of the delta–epsilon definition of limit.
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