Calculus Examples

$lim_{x \to 4} \frac{t^{2} - 3 t - 28}{t^{2 - 16}}$

Step 1

Evaluate the limit of $\frac{t^{2} - 3 t - 28}{t^{2 - 16}}$ which is constant as $x$ approaches $4$ .

$\frac{t^{2} - 3 t - 28}{t^{2 - 16}}$

Step 2

Simplify the answer.

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Step 2.1

Move $t^{2 - 16}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$(t^{2} - 3 t - 28) t^{- (2 - 16)}$

Step 2.2

Subtract $16$ from $2$ .

$(t^{2} - 3 t - 28) t^{- - 14}$

Step 2.3

Multiply $- 1$ by $- 14$ .

$(t^{2} - 3 t - 28) t^{14}$

Step 2.4

Apply the distributive property.

$t^{2} t^{14} - 3 t \cdot t^{14} - 28 t^{14}$

Step 2.5

Simplify.

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Step 2.5.1

Multiply $t^{2}$ by $t^{14}$ by adding the exponents.

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Step 2.5.1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$t^{2 + 14} - 3 t \cdot t^{14} - 28 t^{14}$

Step 2.5.1.2

Add $2$ and $14$ .

$t^{16} - 3 t \cdot t^{14} - 28 t^{14}$

Step 2.5.2

Multiply $t$ by $t^{14}$ by adding the exponents.

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Step 2.5.2.1

Move $t^{14}$ .

$t^{16} - 3 (t^{14} t) - 28 t^{14}$

Step 2.5.2.2

Multiply $t^{14}$ by $t$ .

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Step 2.5.2.2.1

Raise $t$ to the power of $1$ .

$t^{16} - 3 (t^{14} t^{1}) - 28 t^{14}$

Step 2.5.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$t^{16} - 3 t^{14 + 1} - 28 t^{14}$

Step 2.5.2.3

Add $14$ and $1$ .

$t^{16} - 3 t^{15} - 28 t^{14}$