Question

WHAT IS THE VALUE OF m SO THAT THE GIVEN FUNCTION IS CONTINOUS ?

Answer 1

if by m, you mean slope, then any rational number will have a function continuous. Usually, m is used in the function of a straight line, and, most of which, are continuous. the equation of a straight line is: f(x)=mx+b where m is the slop, and b is the y-intercept.

Answer 2

@UnkleRhaukus

Answer 3

you have to make limf(x) as x-> 4- = limf(x) as x -> 4+

Answer 4

one side is 16 and the other is 4m

Answer 5

they should be equal

Answer 6

m=4

Answer 7

yes

Answer 8

But i didnt get how you got 16 and 4m

Answer 9

what is lim(x^2) as x -> 4+ ?

Answer 10

16

Answer 11

so this is the 16 that i wrote

what is lim(mx) as x -> 4-
note here that m is a constant so we can take it out of the limit to get :
m*lim(x) as x->4-

Answer 12

Ok @Cool

Answer 13

So for this piecewise function, the limit of the left side, and the limit of the right side need to equal each other. that is, for the function, x^2 at the point x=4, what is the value? that value needs to match the value of the other function. In otherwords, what does m need to be when 16=m*4?
when both of the piece wise functions are equal, or the left and right limits, the function is continuous.