Calculus Examples

$lim_{t \to 10} \frac{2 {(t - 10)}^{2}}{t}$

Step 1

Move the term $2$ outside of the limit because it is constant with respect to $t$ .

$2 lim_{t \to 10} \frac{{(t - 10)}^{2}}{t}$

Step 2

Split the limit using the Limits Quotient Rule on the limit as $t$ approaches $10$ .

$2 \frac{lim_{t \to 10} {(t - 10)}^{2}}{lim_{t \to 10} t}$

Step 3

Move the exponent $2$ from ${(t - 10)}^{2}$ outside the limit using the Limits Power Rule.

$2 \frac{{(lim_{t \to 10} t - 10)}^{2}}{lim_{t \to 10} t}$

Step 4

Split the limit using the Sum of Limits Rule on the limit as $t$ approaches $10$ .

$2 \frac{{(lim_{t \to 10} t - lim_{t \to 10} 10)}^{2}}{lim_{t \to 10} t}$

Step 5

Evaluate the limit of $10$ which is constant as $t$ approaches $10$ .

$2 \frac{{(lim_{t \to 10} t - 1 \cdot 10)}^{2}}{lim_{t \to 10} t}$

Step 6

Evaluate the limits by plugging in $10$ for all occurrences of $t$ .

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Step 6.1

Evaluate the limit of $t$ by plugging in $10$ for $t$ .

$2 \frac{{(10 - 1 \cdot 10)}^{2}}{lim_{t \to 10} t}$

Step 6.2

Evaluate the limit of $t$ by plugging in $10$ for $t$ .

$2 \frac{{(10 - 1 \cdot 10)}^{2}}{10}$

Step 7

Simplify the answer.

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Step 7.1

Cancel the common factor of $2$ .

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Step 7.1.1

Factor $2$ out of $10$ .

$2 \frac{{(10 - 1 \cdot 10)}^{2}}{2 (5)}$

Step 7.1.2

Cancel the common factor.

$2 \frac{{(10 - 1 \cdot 10)}^{2}}{2 \cdot 5}$

Step 7.1.3

Rewrite the expression.

$\frac{{(10 - 1 \cdot 10)}^{2}}{5}$

Step 7.2

Simplify the numerator.

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Step 7.2.1

Multiply $- 1$ by $10$ .

$\frac{{(10 - 10)}^{2}}{5}$

Step 7.2.2

Subtract $10$ from $10$ .

$\frac{0^{2}}{5}$

Step 7.2.3

Raising $0$ to any positive power yields $0$ .

$\frac{0}{5}$

Step 7.3

Divide $0$ by $5$ .

$0$