Calculus Examples

Evaluate the Limit ( limit as x approaches -9 of x^2-81)/(2x^2+19x+9)
Step 1
Evaluate the limit.
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Step 1.1
Split the limit using the Sum of Limits Rule on the limit as approaches .
Step 1.2
Move the exponent from outside the limit using the Limits Power Rule.
Step 1.3
Evaluate the limit of which is constant as approaches .
Step 2
Evaluate the limit of by plugging in for .
Step 3
Simplify the answer.
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Step 3.1
Simplify the numerator.
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Step 3.1.1
Raise to the power of .
Step 3.1.2
Multiply by .
Step 3.1.3
Subtract from .
Step 3.2
Factor by grouping.
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Step 3.2.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Step 3.2.1.1
Factor out of .
Step 3.2.1.2
Rewrite as plus
Step 3.2.1.3
Apply the distributive property.
Step 3.2.1.4
Multiply by .
Step 3.2.2
Factor out the greatest common factor from each group.
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Step 3.2.2.1
Group the first two terms and the last two terms.
Step 3.2.2.2
Factor out the greatest common factor (GCF) from each group.
Step 3.2.3
Factor the polynomial by factoring out the greatest common factor, .
Step 3.3
Divide by .