Calculus Examples

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

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $- 7$ .

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

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 7$ .

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

Step 3

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

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

Step 4

Evaluate the limits by plugging in $- 7$ for all occurrences of $x$ .

Tap for more steps...

Step 4.1

Evaluate the limit of $x$ by plugging in $- 7$ for $x$ .

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

Step 4.2

Evaluate the limit of $x$ by plugging in $- 7$ for $x$ .

$\frac{- 7}{7 + 7}$

Step 5

Simplify the answer.

Tap for more steps...

Step 5.1

Cancel the common factor of $- 7$ and $7 + 7$ .

Tap for more steps...

Step 5.1.1

Factor $7$ out of $- 7$ .

$\frac{7 \cdot - 1}{7 + 7}$

Step 5.1.2

Cancel the common factors.

Tap for more steps...

Step 5.1.2.1

Factor $7$ out of $7$ .

$\frac{7 \cdot - 1}{7 (1) + 7}$

Step 5.1.2.2

Factor $7$ out of $7$ .

$\frac{7 \cdot - 1}{7 \cdot 1 + 7 \cdot 1}$

Step 5.1.2.3

Factor $7$ out of $7 \cdot 1 + 7 \cdot 1$ .

$\frac{7 \cdot - 1}{7 \cdot (1 + 1)}$

Step 5.1.2.4

Cancel the common factor.

$\frac{7 \cdot - 1}{7 \cdot (1 + 1)}$

Step 5.1.2.5

Rewrite the expression.

$\frac{- 1}{1 + 1}$

Step 5.2

Add $1$ and $1$ .

$\frac{- 1}{2}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$