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.

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Step 2.1

Simplify each term.

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Step 2.1.1

Simplify the numerator.

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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.

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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