Take the limit of the numerator and the limit of the denominator.

Evaluate the limit of by plugging in for .

Evaluate the limit of the denominator.

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

Evaluate the limit of by plugging in for .

The exact value of is .

The expression contains a division by The expression is undefined.

Undefined

The expression contains a division by The expression is undefined.

Undefined

Since is of indeterminate form, apply L’Hospital’s Rule. L’Hospital’s Rule states that the limit of a quotient of functions is equal to the limit of the quotient of their derivatives.

Differentiate the numerator and denominator.

Differentiate using the Power Rule which states that is where .

The derivative of with respect to is .

Convert from to .

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

Evaluate the limit of by plugging in for .

The exact value of is .

Evaluate limit as x approaches 0 of x/(sin(x))