Evaluate limit as x approaches -12 of ( square root of x^2+25-13)/(x+12)

Math
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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Multiply the argument of the limit by the conjugate.
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Combine the opposite terms in .
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Reorder the factors in the terms and .
Subtract from .
Add and .
Simplify each term.
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Multiply .
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Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
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Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify.
Multiply by .
Subtract from .
Take the limit of each term.
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Split the limit using the Sum of Limits Rule on the limit as approaches .
Move the exponent from outside the limit using the Limits Power Rule.
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 .
Simplify the answer.
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Raise to the power of .
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 .
Add and .
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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Rewrite as .
Differentiate using the chain rule, which states that is where and .
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To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
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 .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Move the negative in front of the fraction.
Combine and .
Move to the denominator using the negative exponent rule .
Add and .
Combine and .
Combine and .
Cancel the common factor.
Rewrite the expression.
Since is constant with respect to , the derivative of with respect to is .
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 .
Take the limit of each term.
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Split the limit using the Limits Quotient Rule on the limit as approaches .
Split the limit using the Limits Quotient Rule on the limit as approaches .
Move the exponent from outside the limit using the Limits Power Rule.
Split the limit using the Sum of Limits Rule on the limit as approaches .
Move the exponent from outside the limit using the Limits Power Rule.
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 by plugging in for .
Evaluate the limit of which is constant as approaches .
Evaluate the limit of which is constant as approaches .
Simplify the answer.
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Divide by .
Simplify the denominator.
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Raise to the power of .
Add and .
Rewrite as .
Apply the power rule and multiply exponents, .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Move the negative in front of the fraction.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Evaluate limit as x approaches -12 of ( square root of x^2+25-13)/(x+12)

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