# Evaluate limit as x approaches two hundred twenty-five of ( square root of x minus fifteen) divide(x minus two hundred twenty-five)

Apply L'Hospital's rule.

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.

First, multiply the argument of the limit by the conjugate.

Expand using the FOIL Method.

Use the distributive law.

Apply the distributive property.

Apply the distributive property.

Add the opposite terms in .

Shift the factors in the terms and .

Subtract from .

Add and .

Clarify each term.

Multiply .

Raise to the power of .

Raise to the power of .

Apply the power rule to Add exponents.

Add and .

Should be rewritten as .

Use to rewrite as .

Use the power rule when multiplying the exponents, .

Combine and .

The common factor should be canceled of .

Cancel the common factor.

First, divide by .

Simplify.

Multiply by .

Split the limit using the Sum of Limits Rule on the limit as approaches .

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 .

Subtract from .

Evaluate the limit of the denominator.

Split the limit using the Sum of Limits Rule on the limit as approaches .

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 .

Subtract from .

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.

By the Sum Rule, the derivative of with respect to is .

Evaluate .

Use to rewrite as .

Differentiate using the Power Rule which states that is where .

To write as a fraction with a common denominator, multiply by .

Combine and .

Add numerators over the common denominator.

Clarify the numerator.

Multiply by .

Subtract from .

Put the negative in front of the fraction.

Since is constant with respect to , the derivative of with respect to is .

Reformulate the expression using the negative exponent rule .

Combine terms.

Multiply and .

Add and .

By the Sum Rule, the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Since is constant with respect to , the derivative of with respect to is .

Add and .

Multiply the numerator by the denominator's reciprocal.

Rewrite as .

Multiply by .

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

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

Move the limit under the radical sign.

Evaluate the limit of which is constant as approaches .

Evaluate the limit of by plugging in for .

Clarify the denominator.

Rewrite as .

Withdraw terms from under the radical, assuming positive real numbers.

Multiply .

Multiply and .

First, multiply by .

The result can be displayed in a variety of ways.

Exact Form:

Decimal Form:

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