Calculus Examples

$lim_{x \to - 3} \csc (\frac{3.14 x}{4})$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit inside the trig function because cosecant is continuous.

$\csc (lim_{x \to - 3} \frac{3.14 x}{4})$

Step 1.2

Move the term $\frac{3.14}{4}$ outside of the limit because it is constant with respect to $x$ .

$\csc (\frac{3.14}{4} lim_{x \to - 3} x)$

Step 2

Evaluate the limit of $x$ by plugging in $- 3$ for $x$ .

$\csc (\frac{3.14}{4} \cdot - 3)$

Step 3

Simplify the answer.

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Step 3.1

Divide $3.14$ by $4$ .

$\csc (0.785 \cdot - 3)$

Step 3.2

Multiply $0.785$ by $- 3$ .

$\csc (- 2.355)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\csc (- 2.355)$

Decimal Form:

$- 1.41252732 \dots$