Calculus Examples

$lim_{x \to {(2 π)}^{+}} x \csc (x)$

Step 1

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $2 π$ .

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

Step 2

Evaluate the limit of $x$ by plugging in $2 π$ for $x$ .

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

Step 3

As the $x$ values approach $2 π$ from the right, the function values increase without bound.

$2 π \cdot \infty$

Step 4

Multiply $2 π \infty$ .

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Step 4.1

A non-zero constant times infinity is infinity.

$\infty π$

Step 4.2

A non-zero constant times infinity is infinity.

$\infty$