A community for students.
Here's the question you clicked on:
 0 viewing
Dama28
 2 years ago
The limit represents the derivative of some function f at some number a. State such an f and a.
lim (tan x − 1)/(x − π/4)
(x→π/4)
the answer is f(x) = tan x, a = π/4 but I don't know how to get it. :S
Dama28
 2 years ago
The limit represents the derivative of some function f at some number a. State such an f and a. lim (tan x − 1)/(x − π/4) (x→π/4) the answer is f(x) = tan x, a = π/4 but I don't know how to get it. :S

This Question is Closed

Dama28
 2 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow \frac{ \Pi }{ 4 }} \frac{ \tan(x)1 }{ x\frac{ \Pi }{ 4 } }\]

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1Limit definition of Derivative of a function : \(\huge \lim \limits_{h \rightarrow 0}\dfrac{f(x+h)f(x)}{h}\) Limit definition of Derivative of a function at x=a : \(\huge \lim \limits_{h \rightarrow 0}\dfrac{f(a+h)f(a)}{h}\)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1what you have is : \( \huge \lim \limits_{x \rightarrow \pi/4}\dfrac{\tan x1}{x \pi/4}\) from limit definition i need just h in the denominator, so i can substitute, h = xpi/4 as, x > pi/4, h >0 also, x = pi/4+h so, we have now. \(\huge \lim \limits_{h \rightarrow 0}\dfrac{\tan (\pi/4+h)1}{h}\) comparing this with limit definition, f(a+h) and tan (pi/4+h) we can figure out , f(x) = tan x , and a = pi/4.

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1also, we can confirm it by verifying, f(a) = 1, [comparing tan (pi/4+h)1 with f(a+h)f(a)], f(a)=f(pi/4)=tan (pi/4) = 1 is true.
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.