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Chapter 9: Problem 16

Find the limit. \(\lim _{x \rightarrow 1^{+}} \frac{2+x}{1-x}\)

Short Answer

Expert verified
The limit is \(-\infty\)

Step by step solution

01

Substitute

Substitute x=1 into the expression \(\frac{2+x}{1-x}\).
02

Evaluate

Evaluate the expression with the substituted value. The denominator becomes 0 (since \(1-1=0\)), which makes the fraction undefined.
03

Identify Limit Type

Since the fraction becomes undefined, this suggests a limit that tends to infinity or -infinity. To check whether it is positive or negative infinity, substitute a value slightly greater than 1 (say, 1.01). The value of the denominator will be negative, suggesting that the limit will be negative infinity.

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Most popular questions from this chapter

Compare the values of \(d y\) and \(\Delta y\). \(y=0.5 x^{3} \quad x=2 \quad \Delta x=d x=0.1\)

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