Calculus Examples

Evaluate the Limit limit as x approaches 2 of square root of (5x^2+5)/(9x-2)
Step 1
Move the limit under the radical sign.
Step 2
Split the limit using the Limits Quotient Rule on the limit as approaches .
Step 3
Split the limit using the Sum of Limits Rule on the limit as approaches .
Step 4
Move the term outside of the limit because it is constant with respect to .
Step 5
Move the exponent from outside the limit using the Limits Power Rule.
Step 6
Evaluate the limit of which is constant as approaches .
Step 7
Split the limit using the Sum of Limits Rule on the limit as approaches .
Step 8
Move the term outside of the limit because it is constant with respect to .
Step 9
Evaluate the limit of which is constant as approaches .
Step 10
Evaluate the limits by plugging in for all occurrences of .
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Step 10.1
Evaluate the limit of by plugging in for .
Step 10.2
Evaluate the limit of by plugging in for .
Step 11
Simplify the answer.
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Step 11.1
Raise to the power of .
Step 11.2
Multiply by .
Step 11.3
Add and .
Step 11.4
Multiply by .
Step 11.5
Multiply by .
Step 11.6
Subtract from .
Step 11.7
Rewrite as .
Step 11.8
Simplify the numerator.
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Step 11.8.1
Rewrite as .
Step 11.8.2
Pull terms out from under the radical, assuming positive real numbers.
Step 11.9
Simplify the denominator.
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Step 11.9.1
Rewrite as .
Step 11.9.2
Pull terms out from under the radical, assuming positive real numbers.
Step 12
The result can be shown in multiple forms.
Exact Form:
Decimal Form: