Calculus Examples

Evaluate Using L'Hospital's Rule limit as x approaches 8 of (1+a/x)^(bx)
Step 1
Combine terms.
Tap for more steps...
Step 1.1
Write as a fraction with a common denominator.
Step 1.2
Combine the numerators over the common denominator.
Step 2
Use the properties of logarithms to simplify the limit.
Tap for more steps...
Step 2.1
Rewrite as .
Step 2.2
Expand by moving outside the logarithm.
Step 3
Evaluate the limit.
Tap for more steps...
Step 3.1
Move the limit into the exponent.
Step 3.2
Move the term outside of the limit because it is constant with respect to .
Step 3.3
Split the limit using the Product of Limits Rule on the limit as approaches .
Step 3.4
Move the limit inside the logarithm.
Step 3.5
Split the limit using the Limits Quotient Rule on the limit as approaches .
Step 3.6
Split the limit using the Sum of Limits Rule on the limit as approaches .
Step 3.7
Evaluate the limit of which is constant as approaches .
Step 4
Evaluate the limits by plugging in for all occurrences of .
Tap for more steps...
Step 4.1
Evaluate the limit of by plugging in for .
Step 4.2
Evaluate the limit of by plugging in for .
Step 4.3
Evaluate the limit of by plugging in for .
Step 5
Move to the left of .