Enter a problem...
Calculus Examples
Step 1
Step 1.1
Evaluate the limit of the numerator and the limit of the denominator.
Step 1.1.1
Take the limit of the numerator and the limit of the denominator.
Step 1.1.2
Evaluate the limit of by plugging in for .
Step 1.1.3
Evaluate the limit of the denominator.
Step 1.1.3.1
Move the limit inside the trig function because tangent is continuous.
Step 1.1.3.2
Evaluate the limit of by plugging in for .
Step 1.1.3.3
The exact value of is .
Step 1.1.3.4
The expression contains a division by . The expression is undefined.
Undefined
Step 1.1.4
The expression contains a division by . The expression is undefined.
Undefined
Step 1.2
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.
Step 1.3
Find the derivative of the numerator and denominator.
Step 1.3.1
Differentiate the numerator and denominator.
Step 1.3.2
Differentiate using the Power Rule which states that is where .
Step 1.3.3
The derivative of with respect to is .
Step 2
Step 2.1
Split the limit using the Limits Quotient Rule on the limit as approaches .
Step 2.2
Evaluate the limit of which is constant as approaches .
Step 2.3
Move the exponent from outside the limit using the Limits Power Rule.
Step 2.4
Move the limit inside the trig function because secant is continuous.
Step 3
Evaluate the limit of by plugging in for .
Step 4
Step 4.1
Rewrite as .
Step 4.2
Rewrite as .
Step 4.3
Rewrite in terms of sines and cosines.
Step 4.4
Multiply by the reciprocal of the fraction to divide by .
Step 4.5
Multiply by .
Step 4.6
The exact value of is .
Step 4.7
One to any power is one.