Pre-Algebra Examples

$3038.09 (\frac{1 - {(1 + \frac{0.11}{2})}^{- (12 - x)}}{\frac{0.11}{2}})$

Step 1

Find where the expression $55238 - 55238 \cdot {1.055}^{- 12 + x}$ is undefined.

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Step 2

The vertical asymptotes occur at areas of infinite discontinuity.

No Vertical Asymptotes

Step 3

Evaluate $lim_{x \to - \infty} 55238 - 55238 \cdot {1.055}^{x - 12}$ to find the horizontal asymptote.

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Step 3.1

Evaluate the limit.

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Step 3.1.1

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

$lim_{x \to - \infty} 55238 - lim_{x \to - \infty} 55238 \cdot {1.055}^{x - 12}$

Step 3.1.2

Evaluate the limit of $55238$ which is constant as $x$ approaches $- \infty$ .

$55238 - lim_{x \to - \infty} 55238 \cdot {1.055}^{x - 12}$

Step 3.1.3

Move the term $55238$ outside of the limit because it is constant with respect to $x$ .

$55238 - 55238 lim_{x \to - \infty} {1.055}^{x - 12}$

Step 3.2

Since the exponent $x - 12$ approaches $- \infty$ , the quantity ${1.055}^{x - 12}$ approaches $0$ .

$55238 - 55238 \cdot 0$

Step 3.3

Simplify the answer.

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Step 3.3.1

Multiply $- 55238$ by $0$ .

$55238 + 0$

Step 3.3.2

Add $55238$ and $0$ .

$55238$

Step 4

List the horizontal asymptotes:

$y = 55238$

Step 5

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

Step 6

This is the set of all asymptotes.

No Vertical Asymptotes

Horizontal Asymptotes: $y = 55238$

No Oblique Asymptotes

Step 7