A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
Can someone solve this question please...lim_(x→π/4) (xπ/4)^2/(tanx1)^2 ..
anonymous
 3 years ago
Can someone solve this question please...lim_(x→π/4) (xπ/4)^2/(tanx1)^2 ..

This Question is Open

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0You can try the graphing approach, it will show that it goes towards 0.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0You can solve this problem using l'Hospital's rule. You have to apply the rule twice, because after the first application you still have zero in the numerator and denominator. The second application is a little tricky because the second derivative of\[(\tan x1)^2\]doesn't exactly leap off the page, but when you work through it you'll get a usable result. Post again if this isn't enough help for you to find the answer (which is not zero).

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0There is another approach. First, you can calculate lim_(x→π/4)(xπ/4)/(tanx1). In doing this, you can use a trigonometric equation that tan(a+b)=(tana+tanb)/(1tana*tanb) and convert tanx1 to (tan(xπ/4))*(1+tanx). Therefore the function becomes (xπ/4)*cos(xπ/4)/sin(xπ/4)(1+tanx). When x→π/4, (xπ/4)→0 so lim (xπ/4)/ sin(xπ/4)=1 .All you need then is to plug π/4 into cos(xπ/4)/(1+tanx) which gets 1/2. Square it and you can get the answer 1/4. Hope it helps!

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Creeksider must have been half asleep not to notice that we can avoid the complexity of applying l'Hospital's rule twice by finding the limit of the square root and then squaring the limit. With that insight, though, it seems easier to solve with a single application of l'Hospital's rule than with a trig identity. Working with (xπ/4)/(tanx1), the derivative of the numerator is 1 and the derivative of the denominator is sec²x, so we easily get cos²x. Then the answer is (cos²(π/4))² which is, as WPAN found, 1/4.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.