Calculus Examples

Use the Limit Definition to Find the Derivative
Consider the limit definition of the derivative.
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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Apply the distributive property.
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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Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Multiply by .
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Apply the distributive property.
Multiply by .
Subtract from .
Add and .
Subtract from .
Add and .
Divide by .
Evaluate the limit of which is constant as approaches .
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