Question

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

Short answer

The limit is \(-\infty\)

Step-by-step solution

Substitute

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

Evaluate

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

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.