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

Evaluate limit as x approaches 225 of ( square root of x-15)/(x-225)
Take the limit of each term.
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Apply L'Hospital's rule.
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Evaluate the limit of the numerator and the limit of the denominator.
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Take the limit of the numerator and the limit of the denominator.
Evaluate the limit of the numerator.
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First, multiply the argument of the limit by the conjugate.
Expand using the FOIL Method.
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Use the distributive law.
Apply the distributive property.
Apply the distributive property.
Add the opposite terms in .
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Shift the factors in the terms and .
Subtract from .
Add and .
Clarify each term.
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Multiply .
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Raise to the power of .
Raise to the power of .
Apply the power rule to Add exponents.
Add and .
Should be rewritten as .
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Use to rewrite as .
Use the power rule when multiplying the exponents, .
Combine and .
The common factor should be canceled of .
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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 .
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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.
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Split the limit using the Sum of Limits Rule on the limit as approaches .
Evaluate the limits by plugging in for all occurrences of .
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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.
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Differentiate the numerator and denominator.
By the Sum Rule, the derivative of with respect to is .
Evaluate .
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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.
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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.
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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 limits by plugging in for all occurrences of .
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Evaluate the limit of which is constant as approaches .
Evaluate the limit of by plugging in for .
Clarify the answer.
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Clarify the denominator.
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Rewrite as .
Withdraw terms from under the radical, assuming positive real numbers.
Multiply .
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Multiply and .
First, multiply by .
The result can be displayed in a variety of ways.
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