Calculus Examples

Evaluate the Limit ( limit as x approaches 0 of x^3-6x+8)/(x-2)
Step 1
Split the limit using the Sum of Limits Rule on the limit as approaches .
Step 2
Move the exponent from outside the limit using the Limits Power Rule.
Step 3
Move the term outside of the limit because it is constant with respect to .
Step 4
Evaluate the limit of which is constant as approaches .
Step 5
Evaluate the limits by plugging in for all occurrences of .
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Step 5.1
Evaluate the limit of by plugging in for .
Step 5.2
Evaluate the limit of by plugging in for .
Step 6
Simplify the numerator.
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Step 6.1
Raising to any positive power yields .
Step 6.2
Multiply by .
Step 6.3
Add and .
Step 6.4
Add and .