Calculus Examples

Evaluate the Limit ( limit as x approaches 0 of e^(2x)-e^(-2x)-4x)/(x-sin(x))
Step 1
Split the limit using the Sum of Limits Rule on the limit as approaches .
Step 2
Move the limit into the exponent.
Step 3
Move the term outside of the limit because it is constant with respect to .
Step 4
Move the limit into the exponent.
Step 5
Move the term outside of the limit because it is constant with respect to .
Step 6
Move the term outside of the limit because it is constant with respect to .
Step 7
Evaluate the limits by plugging in for all occurrences of .
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Step 7.1
Evaluate the limit of by plugging in for .
Step 7.2
Evaluate the limit of by plugging in for .
Step 7.3
Evaluate the limit of by plugging in for .
Step 8
Simplify the answer.
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Step 8.1
Simplify the numerator.
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Step 8.1.1
Multiply by .
Step 8.1.2
Anything raised to is .
Step 8.1.3
Multiply by .
Step 8.1.4
Anything raised to is .
Step 8.1.5
Multiply by .
Step 8.1.6
Multiply by .
Step 8.1.7
Add and .
Step 8.1.8
Subtract from .
Step 8.2
Divide by .