Calculus Examples

$lim_{t \to 49} \frac{48.9 - 49}{\sqrt{48.9} - 7}$

Step 1

Evaluate the limit of $\frac{48.9 - 49}{\sqrt{48.9} - 7}$ which is constant as $t$ approaches $49$ .

$\frac{48.9 - 49}{\sqrt{48.9} - 7}$

Step 2

Simplify the answer.

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Step 2.1

Subtract $49$ from $48.9$ .

$\frac{- 0.1}{\sqrt{48.9} - 7}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{0.1}{\sqrt{48.9} - 7}$

Step 2.3

Multiply $\frac{0.1}{\sqrt{48.9} - 7}$ by $\frac{\sqrt{48.9} + 7}{\sqrt{48.9} + 7}$ .

$- (\frac{0.1}{\sqrt{48.9} - 7} \cdot \frac{\sqrt{48.9} + 7}{\sqrt{48.9} + 7})$

Step 2.4

Multiply $\frac{0.1}{\sqrt{48.9} - 7}$ by $\frac{\sqrt{48.9} + 7}{\sqrt{48.9} + 7}$ .

$- \frac{0.1 (\sqrt{48.9} + 7)}{(\sqrt{48.9} - 7) (\sqrt{48.9} + 7)}$

Step 2.5

Expand the denominator using the FOIL method.

$- \frac{0.1 (\sqrt{48.9} + 7)}{{\sqrt{48.9}}^{2} + \sqrt{48.9} \cdot 7 - 7 \sqrt{48.9} - 49}$

Step 2.6

Simplify.

$- \frac{0.1 (\sqrt{48.9} + 7)}{- 0.1}$

Step 2.7

Cancel the common factor of $0.1$ and $- 0.1$ .

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Step 2.7.1

Rewrite $0.1$ as $- 1 (- 0.1)$ .

$- \frac{- 1 (- 0.1) (\sqrt{48.9} + 7)}{- 0.1}$

Step 2.7.2

Cancel the common factor.

$- \frac{- 1 \cdot - 0.1 (\sqrt{48.9} + 7)}{- 0.1}$

Step 2.7.3

Divide $- (\sqrt{48.9} + 7)$ by $1$ .

$- - (\sqrt{48.9} + 7)$

Step 2.8

Apply the distributive property.

$- (- \sqrt{48.9} - 1 \cdot 7)$

Step 2.9

Multiply $- 1$ by $7$ .

$- (- \sqrt{48.9} - 7)$

Step 2.10

Apply the distributive property.

$- - \sqrt{48.9} - - 7$

Step 2.11

Multiply $- - \sqrt{48.9}$ .

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Step 2.11.1

Multiply $- 1$ by $- 1$ .

$1 \sqrt{48.9} - - 7$

Step 2.11.2

Multiply $\sqrt{48.9}$ by $1$ .

$\sqrt{48.9} - - 7$

Step 2.12

Multiply $- 1$ by $- 7$ .

$\sqrt{48.9} + 7$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{48.9} + 7$

Decimal Form:

$13.99285349 \dots$