Calculus Examples

Evaluate the Limit limit as x approaches 2 of (3x^2-6x)/(6x^2+2x)
Step 1
Split the limit using the Limits Quotient Rule on the limit as approaches .
Step 2
Split the limit using the Sum of Limits Rule on the limit as approaches .
Step 3
Move the term outside of the limit because it is constant with respect to .
Step 4
Move the exponent from outside the limit using the Limits Power Rule.
Step 5
Move the term outside of the limit because it is constant with respect to .
Step 6
Split the limit using the Sum of Limits Rule on the limit as approaches .
Step 7
Move the term outside of the limit because it is constant with respect to .
Step 8
Move the exponent from outside the limit using the Limits Power Rule.
Step 9
Move the term outside of the limit because it is constant with respect to .
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 10.3
Evaluate the limit of by plugging in for .
Step 10.4
Evaluate the limit of by plugging in for .
Step 11
Simplify the answer.
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Step 11.1
Cancel the common factor of and .
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Step 11.1.1
Factor out of .
Step 11.1.2
Factor out of .
Step 11.1.3
Factor out of .
Step 11.1.4
Cancel the common factors.
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Step 11.1.4.1
Factor out of .
Step 11.1.4.2
Factor out of .
Step 11.1.4.3
Factor out of .
Step 11.1.4.4
Cancel the common factor.
Step 11.1.4.5
Rewrite the expression.
Step 11.2
Simplify the numerator.
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Step 11.2.1
Multiply by .
Step 11.2.2
Multiply by .
Step 11.2.3
Subtract from .
Step 11.3
Simplify the denominator.
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Step 11.3.1
Raise to the power of .
Step 11.3.2
Multiply by .
Step 11.3.3
Add and .
Step 11.4
Divide by .