Calculus Examples

$lim_{x \to 8} \frac{5000}{4450 - 2 x}$

Step 1

Cancel the common factor of $5000$ and $4450 - 2 x$ .

Tap for more steps...

Step 1.1

Factor $2$ out of $5000$ .

$lim_{x \to 8} \frac{2 (2500)}{4450 - 2 x}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

Factor $2$ out of $4450$ .

$lim_{x \to 8} \frac{2 \cdot 2500}{2 \cdot 2225 - 2 x}$

Step 1.2.2

Factor $2$ out of $- 2 x$ .

$lim_{x \to 8} \frac{2 \cdot 2500}{2 \cdot 2225 + 2 (- x)}$

Step 1.2.3

Factor $2$ out of $2 (2225) + 2 (- x)$ .

$lim_{x \to 8} \frac{2 \cdot 2500}{2 (2225 - x)}$

Step 1.2.4

Cancel the common factor.

$lim_{x \to 8} \frac{2 \cdot 2500}{2 (2225 - x)}$

Step 1.2.5

Rewrite the expression.

$lim_{x \to 8} \frac{2500}{2225 - x}$

Step 2

Move the term $2500$ outside of the limit because it is constant with respect to $x$ .

$2500 lim_{x \to 8} \frac{1}{2225 - x}$

Step 3

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $8$ .

$2500 \frac{lim_{x \to 8} 1}{lim_{x \to 8} 2225 - x}$

Step 4

Evaluate the limit of $1$ which is constant as $x$ approaches $8$ .

$2500 \frac{1}{lim_{x \to 8} 2225 - x}$

Step 5

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $8$ .

$2500 \frac{1}{lim_{x \to 8} 2225 - lim_{x \to 8} x}$

Step 6

Evaluate the limit of $2225$ which is constant as $x$ approaches $8$ .

$2500 \frac{1}{2225 - lim_{x \to 8} x}$

Step 7

Simplify terms.

Tap for more steps...

Step 7.1

Evaluate the limit of $x$ by plugging in $8$ for $x$ .

$2500 \frac{1}{2225 - 8}$

Step 7.2

Simplify the answer.

Tap for more steps...

Step 7.2.1

Subtract $8$ from $2225$ .

$2500 (\frac{1}{2217})$

Step 7.2.2

Combine $2500$ and $\frac{1}{2217}$ .

$\frac{2500}{2217}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{2500}{2217}$

Decimal Form:

$1.12764997 \dots$