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Calculus Examples
Step 1
Divide the numerator and denominator by the highest power of in the denominator, which is .
Step 2
Step 2.1
Simplify each term.
Step 2.1.1
Cancel the common factor of .
Step 2.1.1.1
Cancel the common factor.
Step 2.1.1.2
Rewrite the expression.
Step 2.1.2
Cancel the common factor of and .
Step 2.1.2.1
Factor out of .
Step 2.1.2.2
Cancel the common factors.
Step 2.1.2.2.1
Factor out of .
Step 2.1.2.2.2
Cancel the common factor.
Step 2.1.2.2.3
Rewrite the expression.
Step 2.1.3
Move the negative in front of the fraction.
Step 2.2
Simplify each term.
Step 2.2.1
Cancel the common factor of .
Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Divide by .
Step 2.2.2
Move the negative in front of the fraction.
Step 2.3
Split the limit using the Limits Quotient Rule on the limit as approaches .
Step 2.4
Split the limit using the Sum of Limits Rule on the limit as approaches .
Step 2.5
Evaluate the limit of which is constant as approaches .
Step 2.6
Move the term outside of the limit because it is constant with respect to .
Step 3
Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .
Step 4
Move the term outside of the limit because it is constant with respect to .
Step 5
Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .
Step 6
Step 6.1
Split the limit using the Sum of Limits Rule on the limit as approaches .
Step 6.2
Evaluate the limit of which is constant as approaches .
Step 6.3
Move the term outside of the limit because it is constant with respect to .
Step 7
Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .
Step 8
Step 8.1
Simplify the numerator.
Step 8.1.1
Multiply by .
Step 8.1.2
Multiply by .
Step 8.1.3
Add and .
Step 8.1.4
Add and .
Step 8.2
Simplify the denominator.
Step 8.2.1
Multiply by .
Step 8.2.2
Add and .
Step 9
The result can be shown in multiple forms.
Exact Form:
Decimal Form: