A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
{sin7x/sin6x x not = 0
f(x)={6/7 x=0
is function continuous
anonymous
 3 years ago
{sin7x/sin6x x not = 0 f(x)={6/7 x=0 is function continuous

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@physicsme @shadowfiend @anuragtripathi @daniellemmcqueen @LivForMusic @karatechopper

ujjwal
 3 years ago
Best ResponseYou've already chosen the best response.0Is the question demanding if the function continuous at 0 or not?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Is function is continuous......? @ujjwal

ujjwal
 3 years ago
Best ResponseYou've already chosen the best response.0do you know they define continuity at a point? Here the question should be, "is the function continuous at x=0?"

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes this is the question.... @ujjwal

ujjwal
 3 years ago
Best ResponseYou've already chosen the best response.0To test the continuity of function at x=0, find the limit when x>0 And the find f(0). If \[\\lim_{x \to 0}f(x)=f(0)\] the the function is continuous at x=0

ujjwal
 3 years ago
Best ResponseYou've already chosen the best response.0X tends to 0 when x is not equal to 0

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Lets rewrite the function:\[\frac{\sin(7x)}{\sin(6x)}=\frac{\frac{\sin(7x)}{7x}}{\frac{\sin(6x)}{7x}}\]Now multiply the numerator and denominator by 7/6:\[\frac{\frac{7}{6}\cdot \frac{\sin(7x)}{7x}}{\frac{7}{6}\cdot \frac{\sin(6x)}{7x}}=\frac{\frac{7}{6}\cdot \frac{\sin(7x)}{7x}}{\frac{\sin(6x)}{6x}}\]Now you can take the limit as x goes to 0 using the fact that:

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x\rightarrow 0}\frac{\sin(x)}{x}=1\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0sry, pressed post before i was done.

ujjwal
 3 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \to 0}f(x)=\lim_{x \to 0}\frac{\sin 7x}{\sin 6x}\]\[=\lim_{x \to 0}\frac{\frac{\sin 7x}{7x}}{\frac{\sin 6x}{6x}}\times \frac{6}{7}\]\[=\frac{6}{7}\] Also, f(0)=6/7 since\[\lim_{x \to 0}f(x)=f(0)\]The function is continuous at x=0

ujjwal
 3 years ago
Best ResponseYou've already chosen the best response.0It is already mentioned above but then i would like to post it again. \[\lim_{x \to 0}\frac{\sin \theta}{\theta}=1\]
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.