Calculus Examples

$lim_{x \to 0} \frac{1}{x} + \frac{7 x - 1}{x}$

Step 1

Combine fractions using a common denominator.

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Step 1.1

Combine the numerators over the common denominator.

$lim_{x \to 0} \frac{1 + 7 x - 1}{x}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

Subtract $1$ from $1$ .

$lim_{x \to 0} \frac{7 x + 0}{x}$

Step 1.2.2

Add $7 x$ and $0$ .

$lim_{x \to 0} \frac{7 x}{x}$

Step 1.3

Cancel the common factor of $x$ .

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Step 1.3.1

Cancel the common factor.

$lim_{x \to 0} \frac{7 x}{x}$

Step 1.3.2

Divide $7$ by $1$ .

$lim_{x \to 0} 7$

Step 2

Evaluate the limit of $7$ which is constant as $x$ approaches $0$ .

$7$