Calculus Examples

$lim_{x \to 2 π} x \csc (x)$

Step 1

Change the two-sided limit into a left sided limit.

$lim_{x \to {(2 π)}^{-}} x \csc (x)$

Step 2

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 3

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

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

Step 4

As the $x$ values approach $2 π$ from the left, the function values decrease without bound.

$2 π \cdot - \infty$

Step 5

Multiply $2 π - \infty$ .

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Step 5.1

A non-zero constant times infinity is infinity.

$- \infty π$

Step 5.2

A non-zero constant times infinity is infinity.

$- \infty$