Calculus Examples

$f (0) = 15 \sin (50 π x) + 40 \cos (50 π x)$

Step 1

Replace the variable $x$ with $0$ in the expression.

$f (0) = 15 \sin (50 π (0)) + 40 \cos (50 π (0))$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $50 π (0)$ .

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Step 2.1.1.1

Multiply $0$ by $50$ .

$f (0) = 15 \sin (0 π) + 40 \cos (50 π (0))$

Step 2.1.1.2

Multiply $0$ by $π$ .

$f (0) = 15 \sin (0) + 40 \cos (50 π (0))$

$f (0) = 15 \sin (0) + 40 \cos (50 π (0))$

Step 2.1.2

The exact value of $\sin (0)$ is $0$ .

$f (0) = 15 \cdot 0 + 40 \cos (50 π (0))$

Step 2.1.3

Multiply $15$ by $0$ .

$f (0) = 0 + 40 \cos (50 π (0))$

Step 2.1.4

Multiply $50 π (0)$ .

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Step 2.1.4.1

Multiply $0$ by $50$ .

$f (0) = 0 + 40 \cos (0 π)$

Step 2.1.4.2

Multiply $0$ by $π$ .

$f (0) = 0 + 40 \cos (0)$

$f (0) = 0 + 40 \cos (0)$

Step 2.1.5

The exact value of $\cos (0)$ is $1$ .

$f (0) = 0 + 40 \cdot 1$

Step 2.1.6

Multiply $40$ by $1$ .

$f (0) = 0 + 40$

$f (0) = 0 + 40$

Step 2.2

Add $0$ and $40$ .

$f (0) = 40$

Step 2.3

The final answer is $40$ .

$40$

$40$

Step 3

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$