Question

let f be the function defined by the following.
f(x)= sinx, x<0
x^2, 0 (lessthanorequalto) x< 1
2-x, 1(lessthanorequalto)x<2
x-3 x(greaterthanorequalto)2
For what value of x is f NOT continious?
0 only
1 only
2 only
0 and 2 only
or
0.1.2

Answer 1

\[\lim_{x \rightarrow 2^-}f(x)=\lim_{x \rightarrow 2^-}(2-x)=0\]
\[\lim_{x \rightarrow 2^+}f(x)=\lim_{x \rightarrow 2^+}(x-3)=-1\]
left does not equal right limit
not continuous at 2

Answer 2

do the same thing for 0 and 1
see if left limit=right limit

Answer 3

what do u mean do the same for 0 and 1?

Answer 4

check the left and right limit at 0 and 1 like i did above for 2

Answer 5

(2-x) okay so for limit as x approaches 0, it would be 2..and for 1, the answer is one

Answer 6

left limit at 0 is sin(0)=0
right limit at 0 is (0)^2=0
since left limit=right limit
and f(0)=0
then the function is continuous at 0