Calculus Examples

$lim_{x \to 8} \frac{\sqrt{100 t^{2} - 1000}}{t - 10}$

Step 1

Evaluate the limit of $\frac{\sqrt{100 t^{2} - 1000}}{t - 10}$ which is constant as $x$ approaches $8$ .

$\frac{\sqrt{100 t^{2} - 1000}}{t - 10}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $100$ out of $100 t^{2} - 1000$ .

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Step 2.1.1

Factor $100$ out of $100 t^{2}$ .

$\frac{\sqrt{100 (t^{2}) - 1000}}{t - 10}$

Step 2.1.2

Factor $100$ out of $- 1000$ .

$\frac{\sqrt{100 t^{2} + 100 \cdot - 10}}{t - 10}$

Step 2.1.3

Factor $100$ out of $100 t^{2} + 100 \cdot - 10$ .

$\frac{\sqrt{100 (t^{2} - 10)}}{t - 10}$

Step 2.2

Rewrite $100$ as $10^{2}$ .

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

Step 2.3

Pull terms out from under the radical.

$\frac{10 \sqrt{t^{2} - 10}}{t - 10}$