Calculus Examples

$lim_{x \to π^{+}} \frac{2 \sqrt{x}}{\csc (x)}$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$2 lim_{x \to π^{+}} \frac{\sqrt{x}}{\csc (x)}$

Step 1.2

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $π$ .

$2 \frac{lim_{x \to π^{+}} \sqrt{x}}{lim_{x \to π^{+}} \csc (x)}$

Step 1.3

Move the limit under the radical sign.

$2 \frac{\sqrt{lim_{x \to π^{+}} x}}{lim_{x \to π^{+}} \csc (x)}$

Step 2

Evaluate the limit of $x$ by plugging in $π$ for $x$ .

$2 \frac{\sqrt{π}}{lim_{x \to π^{+}} \csc (x)}$

Step 3

As the $x$ values approach $π$ from the right, the function values decrease without bound.

$2 \frac{\sqrt{π}}{- \infty}$

Step 4

Simplify the answer.

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Step 4.1

Anything finite divided by infinity is zero.

$2 \cdot 0$

Step 4.2

Multiply $2$ by $0$ .

$0$