Calculus Examples

$lim_{x \to - 1} (3 t - 1) (5 t^{2} + 2)$

Step 1

Evaluate the limit of $(3 t - 1) (5 t^{2} + 2)$ which is constant as $x$ approaches $- 1$ .

$(3 t - 1) (5 t^{2} + 2)$

Step 2

Simplify the answer.

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Step 2.1

Expand $(3 t - 1) (5 t^{2} + 2)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

$3 t (5 t^{2} + 2) - 1 (5 t^{2} + 2)$

Step 2.1.2

Apply the distributive property.

$3 t (5 t^{2}) + 3 t \cdot 2 - 1 (5 t^{2} + 2)$

Step 2.1.3

Apply the distributive property.

$3 t (5 t^{2}) + 3 t \cdot 2 - 1 (5 t^{2}) - 1 \cdot 2$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$3 \cdot 5 t \cdot t^{2} + 3 t \cdot 2 - 1 (5 t^{2}) - 1 \cdot 2$

Step 2.2.2

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

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Step 2.2.2.1

Move $t^{2}$ .

$3 \cdot 5 (t^{2} t) + 3 t \cdot 2 - 1 (5 t^{2}) - 1 \cdot 2$

Step 2.2.2.2

Multiply $t^{2}$ by $t$ .

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Step 2.2.2.2.1

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

$3 \cdot 5 (t^{2} t^{1}) + 3 t \cdot 2 - 1 (5 t^{2}) - 1 \cdot 2$

Step 2.2.2.2.2

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

$3 \cdot 5 t^{2 + 1} + 3 t \cdot 2 - 1 (5 t^{2}) - 1 \cdot 2$

Step 2.2.2.3

Add $2$ and $1$ .

$3 \cdot 5 t^{3} + 3 t \cdot 2 - 1 (5 t^{2}) - 1 \cdot 2$

Step 2.2.3

Multiply $3$ by $5$ .

$15 t^{3} + 3 t \cdot 2 - 1 (5 t^{2}) - 1 \cdot 2$

Step 2.2.4

Multiply $2$ by $3$ .

$15 t^{3} + 6 t - 1 (5 t^{2}) - 1 \cdot 2$

Step 2.2.5

Multiply $5$ by $- 1$ .

$15 t^{3} + 6 t - 5 t^{2} - 1 \cdot 2$

Step 2.2.6

Multiply $- 1$ by $2$ .

$15 t^{3} + 6 t - 5 t^{2} - 2$