Use l’Hôpital’s rule to find the limits in Exercises 7–52.
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Question

Use l’Hôpital’s rule to find the limits in Exercises 7–52.

27. lim (x → (π/2)^-) (x - π/2) sec x

Accepted Answer

Welcome back, everyone. Evaluate the limit using Lapital's rule. Limit as x approaches 0 from the right of X multiplied by cosequent of X. A says 1/2, B 0, C1, and D the limit does not exist. Let's begin this problem by rewriting the limit using the definition of code sequent. We're going to get the limit as X approaches 0 from the right of X, multiplied by 1 divided by sin X, right? And now we can write a single fraction, so that is limit as X approaches 0 from the right of X divided by sin X. If we substitute X equals 0, we're going to get 0 in the numerator and sign of 0 in the denominator, which is also 0. This indeterminate form allows us to apply Lappito's rule, and Lapito's rule says that we want to differentiate the numerator and the denominator. So we take the derivative of X and divide by the derivative of sine x. Now, the derivative of X is 1, and the derivative of sine is cosine, so we can just write 1 divided by cosine X. The next step is to substitute X equals 0 again, and we're going to get 1 divided by cosine of 0. Now, cosine of 0. Is going to be equal to one. And we basically get one divided by one, which is now finite. And this is equal to 1, so the limit is equal to 1, which corresponds to the answer choice C. Thank you for watching.

Use l’Hôpital’s rule to find the limits in Exercises 7–52.27. lim (x → (π/2)^-) (x - π/2) sec x

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Use l’Hôpital’s rule to find the limits in Exercises 7–52.
27. lim (x → (π/2)^-) (x - π/2) sec x