Calculus Examples

$lim_{x \to 0} \frac{100}{50 x + 1}$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $100$ outside of the limit because it is constant with respect to $x$ .

$100 lim_{x \to 0} \frac{1}{50 x + 1}$

Step 1.2

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

$100 \frac{lim_{x \to 0} 1}{lim_{x \to 0} 50 x + 1}$

Step 1.3

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

$100 \frac{1}{lim_{x \to 0} 50 x + 1}$

Step 1.4

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

$100 \frac{1}{lim_{x \to 0} 50 x + lim_{x \to 0} 1}$

Step 1.5

Move the term $50$ outside of the limit because it is constant with respect to $x$ .

$100 \frac{1}{50 lim_{x \to 0} x + lim_{x \to 0} 1}$

Step 1.6

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

$100 \frac{1}{50 lim_{x \to 0} x + 1}$

Step 2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$100 \frac{1}{50 \cdot 0 + 1}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the denominator.

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Step 3.1.1

Multiply $50$ by $0$ .

$100 \frac{1}{0 + 1}$

Step 3.1.2

Add $0$ and $1$ .

$100 (\frac{1}{1})$

Step 3.2

Cancel the common factor of $1$ .

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Step 3.2.1

Cancel the common factor.

$100 (\frac{1}{1})$

Step 3.2.2

Rewrite the expression.

$100 \cdot 1$

Step 3.3

Multiply $100$ by $1$ .

$100$