Question

I want solution of this question


Check the continuity of f(x) at x=3 for the function defined as

f(x)={3x+5 if x<3
f(x)=14 if x=3
f(x)=7+21/x if x>3

Answer 1

well, we want to determine if this is going to give us a hole/jump.
So, lets check what happens just above and just below the point:
x= 2, 3, 4
For
f(2) = 3(2)+5 = 9
f(3) = 14
f(4) = 7+ 21/4 = 12.25

Well, it doesnt seem like much of a difference, let's see what all of these eqns do at x=3
3(3)+5 = 14
f(3) = 14
7+21/3 = 14

Looks like this is definitely continuous.

Answer 2

The function is continuous. By definition, a function is continuous if the limit exists and are the same at a point approaching from both directions (i.e. from below or the left and above or the right), and the evaluated function is the same as the limit at that point.

Answer 3

for aamir9119....agreena have answer our question...so juz follow ok