Calculus Examples

$f (t) = 2 t^{2} - 5$ , $[5, 5.1]$

Step 1

Divide each term in $f t = 2 t^{2} - 5$ by $t$ and simplify.

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Step 1.1

Divide each term in $f t = 2 t^{2} - 5$ by $t$ .

$\frac{f t}{t} = \frac{2 t^{2}}{t} + \frac{- 5}{t}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $t$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{f t}{t} = \frac{2 t^{2}}{t} + \frac{- 5}{t}$

Step 1.2.1.2

Divide $f$ by $1$ .

$f = \frac{2 t^{2}}{t} + \frac{- 5}{t}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Cancel the common factor of $t^{2}$ and $t$ .

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Step 1.3.1.1.1

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

$f = \frac{t (2 t)}{t} + \frac{- 5}{t}$

Step 1.3.1.1.2

Cancel the common factors.

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Step 1.3.1.1.2.1

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

$f = \frac{t (2 t)}{t^{1}} + \frac{- 5}{t}$

Step 1.3.1.1.2.2

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

$f = \frac{t (2 t)}{t \cdot 1} + \frac{- 5}{t}$

Step 1.3.1.1.2.3

Cancel the common factor.

$f = \frac{t (2 t)}{t \cdot 1} + \frac{- 5}{t}$

Step 1.3.1.1.2.4

Rewrite the expression.

$f = \frac{2 t}{1} + \frac{- 5}{t}$

Step 1.3.1.1.2.5

Divide $2 t$ by $1$ .

$f = 2 t + \frac{- 5}{t}$

Step 1.3.1.2

Move the negative in front of the fraction.

$f = 2 t - \frac{5}{t}$

Step 2

The equation can not be solved. The given interval accounts for only one variable, but $2$ are present in the equation $f = 2 t - \frac{5}{t}$ .

No solution