Question

{sin7x/sin6x x not = 0
f(x)={6/7 x=0
is function continuous

Answer 1

@physicsme @shadowfiend @anuragtripathi @daniellemmcqueen @LivForMusic @karatechopper

Answer 2

@ujjwal

Answer 3

@ujjwal

Answer 4

@supercrazy92

Answer 5

Is the question demanding if the function continuous at 0 or not?

Answer 6

Is function is continuous......? @ujjwal

Answer 7

do you know they define continuity at a point? Here the question should be, "is the function continuous at x=0?"

Answer 8

yes this is the question.... @ujjwal

Answer 9

To 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

Answer 10

X tends to 0 when x is not equal to 0

Answer 11

Lets re-write 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:

Answer 12

\[\lim_{x\rightarrow 0}\frac{\sin(x)}{x}=1\]

Answer 13

sry, pressed post before i was done.

Answer 14

\[\lim_{x \to 0}f(x)=\lim_{x \to 0}\frac{\sin 7x}{\sin 6x}\]\[=\lim_{x \to 0}\frac{\frac{\sin 7x}{7x}}{\frac{\sin 6x}{6x}}\times \frac{6}{7}\]\[=\frac{6}{7}\]
Also, f(0)=6/7
since\[\lim_{x \to 0}f(x)=f(0)\]The function is continuous at x=0

Answer 15

It is already mentioned above but then i would like to post it again. \[\lim_{x \to 0}\frac{\sin \theta}{\theta}=1\]