Calculus Examples

Evaluate the limit of the numerator and the limit of the denominator.
Since is of indeterminate form, apply L'Hospital's Rule. L'Hospital's Rule states that the limit of a quotient of functions is equal to the limit of the quotient of their derivatives.
Find the derivative of the numerator and denominator.
Take the limit of each term.
Tap for more steps...
Split the limit using the Limits Quotient Rule on the limit as approaches .
Split the limit using the Sum of Limits Rule on the limit as approaches .
Move the term outside of the limit because it is constant with respect to .
Move the exponent from outside the limit using the Limits Power Rule.
Split the limit using the Sum of Limits Rule on the limit as approaches .
Move the term outside of the limit because it is constant with respect to .
Move the exponent from outside the limit using the Limits Power Rule.
Move the term outside of the limit because it is constant with respect to .
Evaluate the limits by plugging in for all occurrences of .
Tap for more steps...
Evaluate the limit of by plugging in for .
Evaluate the limit of which is constant as approaches .
Evaluate the limit of by plugging in for .
Evaluate the limit of by plugging in for .
Evaluate the limit of which is constant as approaches .
Simplify the answer.
Tap for more steps...
Simplify the numerator.
Tap for more steps...
Use the power rule to combine exponents.
Add and to get .
Raise to the power of to get .
Subtract from to get .
Simplify the denominator.
Tap for more steps...
Rewrite.
Evaluate the limit of the numerator and the limit of the denominator.
Tap for more steps...
Take the limit of the numerator and the limit of the denominator.
Evaluate the limit of the numerator.
Tap for more steps...
Take the limit of each term.
Tap for more steps...
Split the limit using the Sum of Limits Rule on the limit as approaches .
Move the exponent from outside the limit using the Limits Power Rule.
Move the term outside of the limit because it is constant with respect to .
Evaluate the limits by plugging in for all occurrences of .
Tap for more steps...
Evaluate the limit of by plugging in for .
Evaluate the limit of by plugging in for .
Evaluate the limit of which is constant as approaches .
Simplify the answer.
Tap for more steps...
Simplify each term.
Tap for more steps...
Remove parentheses around .
Raise to the power of to get .
Multiply by to get .
Subtract from to get .
Subtract from to get .
Evaluate the limit of the denominator.
Tap for more steps...
Take the limit of each term.
Tap for more steps...
Split the limit using the Sum of Limits Rule on the limit as approaches .
Move the exponent from outside the limit using the Limits Power Rule.
Move the exponent from outside the limit using the Limits Power Rule.
Move the term outside of the limit because it is constant with respect to .
Evaluate the limits by plugging in for all occurrences of .
Tap for more steps...
Evaluate the limit of by plugging in for .
Evaluate the limit of by plugging in for .
Evaluate the limit of by plugging in for .
Evaluate the limit of which is constant as approaches .
Simplify the answer.
Tap for more steps...
Simplify each term.
Tap for more steps...
Remove parentheses around .
Raise to the power of to get .
Remove parentheses around .
Raise to the power of to get .
Multiply by to get .
Add and to get .
Subtract from to get .
Subtract from to get .
The expression contains a division by . The expression is undefined.
Undefined
The expression contains a division by . The expression is undefined.
Undefined
The expression contains a division by . The expression is undefined.
Undefined
Since is of indeterminate form, apply L'Hospital's Rule. L'Hospital's Rule states that the limit of a quotient of functions is equal to the limit of the quotient of their derivatives.
Find the derivative of the numerator and denominator.
Tap for more steps...
Rewrite.
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Evaluate .
Tap for more steps...
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by to get .
Since is constant with respect to , the derivative of with respect to is .
Add and to get .
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Differentiate using the Power Rule which states that is where .
Evaluate .
Tap for more steps...
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by to get .
Since is constant with respect to , the derivative of with respect to is .
Add and to get .
Rewrite.
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Differentiate using the Power Rule which states that is where .
Evaluate .
Since is constant with respect to , the derivative of with respect to is .
Add and to get .
Split the limit using the Sum of Limits Rule on the limit as approaches .
Move the term outside of the limit because it is constant with respect to .
Move the exponent from outside the limit using the Limits Power Rule.
Move the term outside of the limit because it is constant with respect to .
Evaluate the limit of by plugging in for .
Evaluate the limit of by plugging in for .
Evaluate the limit of which is constant as approaches .
Use the power rule to combine exponents.
Add and to get .
Raise to the power of to get .
Multiply by to get .
Add and to get .
Subtract from to get .
Enter YOUR Problem

Enter the email address associated with your Mathway account below and we'll send you a link to reset your password.

Please enter an email address
Please enter a valid email address
The email address you entered was not found in our system
The email address you entered is associated with a Facebook user
We're sorry, we were unable to process your request at this time

Mathway Premium

Step-by-step work + explanations
  •    Step-by-step work
  •    Detailed explanations
  •    No advertisements
  •    Access anywhere
Access the steps on both the Mathway website and mobile apps
$--.--/month
$--.--/year (--%)

Mathway Premium

Visa and MasterCard security codes are located on the back of card and are typically a separate group of 3 digits to the right of the signature strip.

American Express security codes are 4 digits located on the front of the card and usually towards the right.
This option is required to subscribe.
Go Back

Step-by-step upgrade complete!

Mathway requires javascript and a modern browser.
  [ x 2     1 2     π     x d x   ]