Calculus Examples

$lim_{x \to 0} 1 + \frac{1}{x}$

Step 1

Change the two-sided limit into a left sided limit.

$lim_{x \to 0^{-}} 1 + \frac{1}{x}$

Step 2

Evaluate the limit.

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Step 2.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $0$ .

$lim_{x \to 0^{-}} 1 + lim_{x \to 0^{-}} \frac{1}{x}$

Step 2.2

Evaluate the limit of $1$ which is constant as $x$ approaches $0$ .

$1 + lim_{x \to 0^{-}} \frac{1}{x}$

Step 3

Since the numerator is a constant and the denominator approaches $0$ when $x$ approaches $0$ from the left, the fraction $\frac{1}{x}$ approaches negative infinity.

$1 + - \infty$

Step 4

Infinity plus or minus a number is infinity.

$- \infty$