Calculus Examples

$f (0.29) = x - \frac{x^{3} + 3 x^{2} - 2 x - 1}{3 x^{2} + 6 x - 2}$

Step 1

Replace the variable

$x$ with

$0.29$ in the expression.

$f (0.29) = (0.29) - \frac{{(0.29)}^{3} + 3 {(0.29)}^{2} - 2 \cdot 0.29 - 1}{3 {(0.29)}^{2} + 6 (0.29) - 2}$

Step 2

Simplify the result.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Simplify the numerator.

Tap for more steps...

Step 2.1.1.1

Raise

$0.29$ to the power of

$3$ .

$f (0.29) = 0.29 - \frac{0.024389 + 3 \cdot {0.29}^{2} - 2 \cdot 0.29 - 1}{3 \cdot {0.29}^{2} + 6 (0.29) - 2}$

Step 2.1.1.2

Raise

$0.29$ to the power of

$2$ .

$f (0.29) = 0.29 - \frac{0.024389 + 3 \cdot 0.0841 - 2 \cdot 0.29 - 1}{3 \cdot {0.29}^{2} + 6 (0.29) - 2}$

Step 2.1.1.3

Multiply

$3$ by

$0.0841$ .

$f (0.29) = 0.29 - \frac{0.024389 + 0.2523 - 2 \cdot 0.29 - 1}{3 \cdot {0.29}^{2} + 6 (0.29) - 2}$

Step 2.1.1.4

Multiply

$- 2$ by

$0.29$ .

$f (0.29) = 0.29 - \frac{0.024389 + 0.2523 - 0.58 - 1}{3 \cdot {0.29}^{2} + 6 (0.29) - 2}$

Step 2.1.1.5

Add

$0.024389$ and

$0.2523$ .

$f (0.29) = 0.29 - \frac{0.276689 - 0.58 - 1}{3 \cdot {0.29}^{2} + 6 (0.29) - 2}$

Step 2.1.1.6

Subtract

$0.58$ from

$0.276689$ .

$f (0.29) = 0.29 - \frac{- 0.303311 - 1}{3 \cdot {0.29}^{2} + 6 (0.29) - 2}$

Step 2.1.1.7

Subtract

$1$ from

$- 0.303311$ .

$f (0.29) = 0.29 - \frac{- 1.303311}{3 \cdot {0.29}^{2} + 6 (0.29) - 2}$

Step 2.1.2

Simplify the denominator.

Tap for more steps...

Step 2.1.2.1

Raise

$0.29$ to the power of

$2$ .

$f (0.29) = 0.29 - \frac{- 1.303311}{3 \cdot 0.0841 + 6 (0.29) - 2}$

Step 2.1.2.2

Multiply

$3$ by

$0.0841$ .

$f (0.29) = 0.29 - \frac{- 1.303311}{0.2523 + 6 (0.29) - 2}$

Step 2.1.2.3

Multiply

$6$ by

$0.29$ .

$f (0.29) = 0.29 - \frac{- 1.303311}{0.2523 + 1.74 - 2}$

Step 2.1.2.4

Add

$0.2523$ and

$1.74$ .

$f (0.29) = 0.29 - \frac{- 1.303311}{1.9923 - 2}$

Step 2.1.2.5

Subtract

$2$ from

$1.9923$ .

$f (0.29) = 0.29 - \frac{- 1.303311}{- 0.0077}$

Step 2.1.3

Divide

$- 1.303311$ by

$- 0.0077$ .

$f (0.29) = 0.29 - 1 \cdot 169.26116883$

Step 2.1.4

Multiply

$- 1$ by

$169.26116883$ .

$f (0.29) = 0.29 - 169.26116883$

Step 2.2

Subtract

$169.26116883$ from

$0.29$ .

$f (0.29) = - 168.97116883$

Step 2.3

The final answer is

$- 168.97116883$ .

$- 168.97116883$

Step 3