Evaluate Using L’Hospital’s Rule limit as x approaches infinity of x/( square root of x^2+1)

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.
The limit at infinity of a polynomial whose leading coefficient is positive is infinity.
As approaches for radicals, the value goes to .
Infinity divided by infinity 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.
Differentiate using the Power Rule which states that is where .
Use to 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 .
To write as a fraction with a common denominator, multiply by .
Combine and .
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 .
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 .
Combine and .
Combine and .
Cancel the common factor.
Rewrite the expression.
Multiply the numerator by the reciprocal of the denominator.
Rewrite as .
Multiply by .
Take the limit of each term.
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Divide the numerator and denominator by the highest power of in the denominator, which is .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Split the limit using the Limits Quotient Rule on the limit as approaches .
Move the limit under the radical sign.
Split the limit using the Sum of Limits Rule on the limit as approaches .
Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .
Evaluate the limits by plugging in the value for the variable.
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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 .
Add and .
Any root of is .
Evaluate Using L’Hospital’s Rule limit as x approaches infinity of x/( square root of x^2+1)

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