Calculus Examples

$\frac{lim_{x \to 3.99} x - 4}{x^{2} - 3 x - 4}$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $3.99$ .

$\frac{lim_{x \to 3.99} x - lim_{x \to 3.99} 4}{x^{2} - 3 x - 4}$

Step 1.2

Evaluate the limit of $4$ which is constant as $x$ approaches $3.99$ .

$\frac{lim_{x \to 3.99} x - 1 \cdot 4}{x^{2} - 3 x - 4}$

Step 2

Evaluate the limit of $x$ by plugging in $3.99$ for $x$ .

$\frac{3.99 - 1 \cdot 4}{x^{2} - 3 x - 4}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Multiply $- 1$ by $4$ .

$\frac{3.99 - 4}{x^{2} - 3 x - 4}$

Step 3.1.2

Subtract $4$ from $3.99$ .

$\frac{- 0.01}{x^{2} - 3 x - 4}$

Step 3.2

Factor $x^{2} - 3 x - 4$ using the AC method.

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Step 3.2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 4$ and whose sum is $- 3$ .

$- 4, 1$

Step 3.2.2

Write the factored form using these integers.

$\frac{- 0.01}{(x - 4) (x + 1)}$

Step 3.3

Move the negative in front of the fraction.

$- \frac{0.01}{(x - 4) (x + 1)}$