Calculus Examples

$lim_{x \to 4.00001} \frac{x}{x - 4}$

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $4.00001$ .

$\frac{lim_{x \to 4.00001} x}{lim_{x \to 4.00001} x - 4}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $4.00001$ .

$\frac{lim_{x \to 4.00001} x}{lim_{x \to 4.00001} x - lim_{x \to 4.00001} 4}$

Step 3

Evaluate the limit of $4$ which is constant as $x$ approaches $4.00001$ .

$\frac{lim_{x \to 4.00001} x}{lim_{x \to 4.00001} x - 1 \cdot 4}$

Step 4

Evaluate the limits by plugging in $4.00001$ for all occurrences of $x$ .

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Step 4.1

Evaluate the limit of $x$ by plugging in $4.00001$ for $x$ .

$\frac{4.00001}{lim_{x \to 4.00001} x - 1 \cdot 4}$

Step 4.2

Evaluate the limit of $x$ by plugging in $4.00001$ for $x$ .

$\frac{4.00001}{4.00001 - 1 \cdot 4}$

Step 5

Simplify the answer.

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Step 5.1

Simplify the denominator.

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Step 5.1.1

Multiply $- 1$ by $4$ .

$\frac{4.00001}{4.00001 - 4}$

Step 5.1.2

Subtract $4$ from $4.00001$ .

$\frac{4.00001}{0.00001}$

Step 5.2

Divide $4.00001$ by $0.00001$ .

$400001$