- If we take the limit as x goes to 0, we get an indeterminate form , so let’s use L’Hôpital’s
Rule. We take the derivative of the numerator and the denominator and we get
= . Now, when we take the limit we get
.
If we take the limit as x goes to 0, we get an indeterminate form , so let’s use L’Hôpital’s
Rule. We take the derivative of the numerator and the denominator and we get
= = . Let’s use
some trig identities to simplify the numerator and denominator. We know that 1 − cos^2 θ = sin^2
θ and sec^2 θ − 1 = tan^2 θ. We get = = .
Next, substitute for tan^2 θ: = . Now, when we
take the limit we get 2cos^2 θ = 2.
SOLUTIONS TO PRACTICE PROBLEM SET 18
1.
Here we will use the Power Rule, which says that . The integral is
= + C.
2. 10 + C
Here we will use the Power Rule, which says that . The integral is
= = .
