Calculus Examples

$lim_{x \to 8} \frac{t - t \sqrt{t}}{2 t^{\frac{3}{2}} + 3 t - 5}$

Step 1

Evaluate the limit of $\frac{t - t \sqrt{t}}{2 t^{\frac{3}{2}} + 3 t - 5}$ which is constant as $x$ approaches $8$ .

$\frac{t - t \sqrt{t}}{2 t^{\frac{3}{2}} + 3 t - 5}$

Step 2

Simplify the answer.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Factor $t$ out of $t - t \sqrt{t}$ .

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Step 2.1.1.1

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

$\frac{t^{1} - t \sqrt{t}}{2 t^{\frac{3}{2}} + 3 t - 5}$

Step 2.1.1.2

Factor $t$ out of $t^{1}$ .

$\frac{t \cdot 1 - t \sqrt{t}}{2 t^{\frac{3}{2}} + 3 t - 5}$

Step 2.1.1.3

Factor $t$ out of $- t \sqrt{t}$ .

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

Step 2.1.1.4

Factor $t$ out of $t \cdot 1 + t (- 1 \sqrt{t})$ .

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

Step 2.1.2

Rewrite $- 1 \sqrt{t}$ as $- \sqrt{t}$ .

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

Step 2.2

Reorder terms.

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