Calculus Examples

$lim_{t \to \infty} \frac{mg}{c} (1 - e^{- \frac{c t}{m}})$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $\frac{mg}{c}$ outside of the limit because it is constant with respect to $t$ .

$\frac{mg}{c} lim_{t \to \infty} 1 - e^{- \frac{c t}{m}}$

Step 1.2

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

$\frac{mg}{c} (lim_{t \to \infty} 1 - lim_{t \to \infty} e^{- \frac{c t}{m}})$

Step 1.3

Evaluate the limit of $1$ which is constant as $t$ approaches $\infty$ .

$\frac{mg}{c} (1 - lim_{t \to \infty} e^{- \frac{c t}{m}})$

Step 2

Since the exponent $- \frac{c t}{m}$ approaches $- \infty$ , the quantity $e^{- \frac{c t}{m}}$ approaches $0$ .

$\frac{mg}{c} (1 - 0)$

Step 3

Simplify the answer.

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Step 3.1

Rewrite the expression.

$\frac{1}{c} mg (1 - 0)$

Step 3.2

Subtract $0$ from $1$ .

$\frac{1}{c} mg \cdot 1$

Step 3.3

Multiply $\frac{1}{c}$ by $1$ .

$\frac{1}{c} mg$