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Calculus Examples
Step 1
Step 1.1
Apply the distributive property.
Step 1.2
Rewrite using the commutative property of multiplication.
Step 1.3
Move to the left of .
Step 1.4
Multiply by by adding the exponents.
Step 1.4.1
Move .
Step 1.4.2
Multiply by .
Step 1.4.2.1
Raise to the power of .
Step 1.4.2.2
Use the power rule to combine exponents.
Step 1.4.3
Add and .
Step 2
Divide the numerator and denominator by the highest power of in the denominator, which is .
Step 3
Step 3.1
Cancel the common factor of .
Step 3.1.1
Cancel the common factor.
Step 3.1.2
Rewrite the expression.
Step 3.2
Simplify each term.
Step 3.2.1
Cancel the common factor of .
Step 3.2.1.1
Cancel the common factor.
Step 3.2.1.2
Divide by .
Step 3.2.2
Cancel the common factor of and .
Step 3.2.2.1
Factor out of .
Step 3.2.2.2
Cancel the common factors.
Step 3.2.2.2.1
Factor out of .
Step 3.2.2.2.2
Cancel the common factor.
Step 3.2.2.2.3
Rewrite the expression.
Step 3.3
Split the limit using the Limits Quotient Rule on the limit as approaches .
Step 3.4
Split the limit using the Sum of Limits Rule on the limit as approaches .
Step 3.5
Evaluate the limit of which is constant as approaches .
Step 3.6
Move the term outside of the limit because it is constant with respect to .
Step 4
Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .
Step 5
Step 5.1
Split the limit using the Sum of Limits Rule on the limit as approaches .
Step 5.2
Evaluate the limit of which is constant as approaches .
Step 5.3
Move the term outside of the limit because it is constant with respect to .
Step 6
Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .
Step 7
Step 7.1
Simplify the numerator.
Step 7.1.1
Multiply by .
Step 7.1.2
Add and .
Step 7.2
Simplify the denominator.
Step 7.2.1
Multiply by .
Step 7.2.2
Add and .
Step 8
The result can be shown in multiple forms.
Exact Form:
Decimal Form: