Question

find whether continuous or not at x=0
f(x) = |x| cos(1/x), if x<>0
0, if x=0

Answer 1

so u need to find if the lim when x-> 0 of the function is equal to the value of the function whne x=0

Answer 2

yes

Answer 3

OK THE VALUE OF THE FUNCTION whne x= 0 is
0
and the limit of the function when x-> 0 is??

Answer 4

did u get what is the limit for this?

Answer 5

Similarly I have one more problem of same type
\[f(x) = |x-a| \sin(1/(x-a)), if x \neq 0\]
0 if x=0 , Find f(x) is continuous or not at x=a?

Answer 6

please anyone help me

Answer 7

use the squeeze theorem