# Evaluate limit as x approaches zero of (sin(x)) divide(five x)

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

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 the numerator.

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

Evaluate the limit of by plugging in for .

The exact value of is .

Evaluate the limit of by plugging in for .

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.

The derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Take the limit of each term.

Split the limit using the Limits Quotient Rule on the limit as approaches .

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

Evaluate the limits by plugging in for all occurrences of .

Evaluate the limit of by plugging in for .

Evaluate the limit of which is constant as approaches .

Simplify the answer.

Divide by .

The exact value of is .

Multiply by .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

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