Calculus Examples

Find the Difference Quotient
Consider the difference quotient formula. Use this formula to solve for the slope of the secant line .
Find the components of the definition.
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Evaluate the function at .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Rewrite as .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Remove parentheses.
Simplify and combine like terms.
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Simplify each term.
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Use the power rule to combine exponents.
Add and to get .
Use the power rule to combine exponents.
Add and to get .
Add and to get .
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Reorder and .
Add and to get .
Apply the distributive property.
Multiply by to get .
Remove parentheses around .
Apply the distributive property.
Remove unnecessary parentheses.
The final answer is .
Find the components of the definition.
Plug in the components.
Simplify.
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Simplify the numerator.
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Apply the distributive property.
Simplify.
Move parentheses.
Remove parentheses.
Subtract from to get .
Add and to get .
Subtract from to get .
Add and to get .
Add and to get .
Add and to get .
Factor out of .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by to get .
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