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

Evaluate the limit of the numerator and the limit of the denominator.
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.
Find the derivative of the numerator and denominator.
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))