Calculus Examples

$lim_{x \to 8} \frac{1350}{1 + 4.2 {(1.7)}^{- x}}$

Step 1

Move the term $1350$ outside of the limit because it is constant with respect to $x$ .

$1350 lim_{x \to 8} \frac{1}{1 + 4.2 {(1.7)}^{- x}}$

Step 2

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

$1350 \frac{lim_{x \to 8} 1}{lim_{x \to 8} 1 + 4.2 {(1.7)}^{- x}}$

Step 3

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

$1350 \frac{1}{lim_{x \to 8} 1 + 4.2 {(1.7)}^{- x}}$

Step 4

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

$1350 \frac{1}{lim_{x \to 8} 1 + lim_{x \to 8} 4.2 {(1.7)}^{- x}}$

Step 5

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

$1350 \frac{1}{1 + lim_{x \to 8} 4.2 {(1.7)}^{- x}}$

Step 6

Move the term $4.2$ outside of the limit because it is constant with respect to $x$ .

$1350 \frac{1}{1 + 4.2 lim_{x \to 8} {(1.7)}^{- x}}$

Step 7

Move the limit into the exponent.

$1350 \frac{1}{1 + 4.2 \cdot {1.7}^{lim_{x \to 8} - x}}$

Step 8

Move the term $- 1$ outside of the limit because it is constant with respect to $x$ .

$1350 \frac{1}{1 + 4.2 \cdot {1.7}^{- lim_{x \to 8} x}}$

Step 9

Simplify terms.

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Step 9.1

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

$1350 \frac{1}{1 + 4.2 \cdot {1.7}^{- 8}}$

Step 9.2

Simplify the answer.

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Step 9.2.1

Simplify the denominator.

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Step 9.2.1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$1350 \frac{1}{1 + 4.2 \cdot \frac{1}{{1.7}^{8}}}$

Step 9.2.1.2

Raise $1.7$ to the power of $8$ .

$1350 \frac{1}{1 + 4.2 \cdot \frac{1}{69.75757441}}$

Step 9.2.1.3

Divide $1$ by $69.75757441$ .

$1350 \frac{1}{1 + 4.2 \cdot 0.01433536}$

Step 9.2.1.4

Multiply $4.2$ by $0.01433536$ .

$1350 \frac{1}{1 + 0.06020851}$

Step 9.2.1.5

Add $1$ and $0.06020851$ .

$1350 (\frac{1}{1.06020851})$

Step 9.2.2

Divide $1$ by $1.06020851$ .

$1350 \cdot 0.94321068$

Step 9.2.3

Multiply $1350$ by $0.94321068$ .

$1273.33442456$