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

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

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

ujjwal
 2 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?"

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

ujjwal
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0X tends to 0 when x is not equal to 0

joemath314159
 2 years ago
Best ResponseYou've already chosen the best response.1Lets 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:

joemath314159
 2 years ago
Best ResponseYou've already chosen the best response.1\[\lim_{x\rightarrow 0}\frac{\sin(x)}{x}=1\]

joemath314159
 2 years ago
Best ResponseYou've already chosen the best response.1sry, pressed post before i was done.

ujjwal
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0It is already mentioned above but then i would like to post it again. \[\lim_{x \to 0}\frac{\sin \theta}{\theta}=1\]
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