Calculus Examples

$lim_{x \to \infty} \frac{t^{2} + 3.3 t + 50}{0.1 t^{2} - 1.5 t + 13}$

Step 1

Evaluate the limit of $\frac{t^{2} + 3.3 t + 50}{0.1 t^{2} - 1.5 t + 13}$ which is constant as $x$ approaches $\infty$ .

$\frac{t^{2} + 3.3 t + 50}{0.1 t^{2} - 1.5 t + 13}$

Step 2

Simplify the answer.

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Step 2.1

Factor $0.1$ out of $0.1 t^{2} - 1.5 t + 13$ .

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Step 2.1.1

Factor $0.1$ out of $0.1 t^{2}$ .

$\frac{t^{2} + 3.3 t + 50}{0.1 (t^{2}) - 1.5 t + 13}$

Step 2.1.2

Factor $0.1$ out of $- 1.5 t$ .

$\frac{t^{2} + 3.3 t + 50}{0.1 (t^{2}) + 0.1 (- 15 t) + 13}$

Step 2.1.3

Factor $0.1$ out of $13$ .

$\frac{t^{2} + 3.3 t + 50}{0.1 t^{2} + 0.1 (- 15 t) + 0.1 \cdot 130}$

Step 2.1.4

Factor $0.1$ out of $0.1 t^{2} + 0.1 (- 15 t)$ .

$\frac{t^{2} + 3.3 t + 50}{0.1 (t^{2} - 15 t) + 0.1 \cdot 130}$

Step 2.1.5

Factor $0.1$ out of $0.1 (t^{2} - 15 t) + 0.1 \cdot 130$ .

$\frac{t^{2} + 3.3 t + 50}{0.1 (t^{2} - 15 t + 130)}$

Step 2.2

Multiply by $1$ .

$\frac{1 t^{2} + 3.3 t + 50}{0.1 (t^{2} - 15 t + 130)}$

Step 2.3

Factor $1$ out of $3.3 t$ .

$\frac{1 t^{2} + 1 (3.3 t) + 50}{0.1 (t^{2} - 15 t + 130)}$

Step 2.4

Factor $1$ out of $1 t^{2} + 1 (3.3 t)$ .

$\frac{1 (t^{2} + 3.3 t) + 50}{0.1 (t^{2} - 15 t + 130)}$

Step 2.5

Rewrite $50$ as $1 (50)$ .

$\frac{1 (t^{2} + 3.3 t) + 1 (50)}{0.1 (t^{2} - 15 t + 130)}$

Step 2.6

Factor $1$ out of $1 (t^{2} + 3.3 t) + 1 (50)$ .

$\frac{1 (t^{2} + 3.3 t + 50)}{0.1 (t^{2} - 15 t + 130)}$

Step 2.7

Separate fractions.

$\frac{1}{0.1} \cdot \frac{t^{2} + 3.3 t + 50}{t^{2} - 15 t + 130}$

Step 2.8

Divide $1$ by $0.1$ .

$10 \frac{t^{2} + 3.3 t + 50}{t^{2} - 15 t + 130}$

Step 2.9

Combine $10$ and $\frac{t^{2} + 3.3 t + 50}{t^{2} - 15 t + 130}$ .

$\frac{10 (t^{2} + 3.3 t + 50)}{t^{2} - 15 t + 130}$