Question

In each case below, define f(0) so that the function f becomes continuous at 0

f(x)=x^3+5 x=/0

Answer 1

for continuity, the limit of the function at that point and the value of the function at that point must be equal. So lim x->0 f(x)=5 and hence we must define f(0)=5

Answer 2

@jbn123

Answer 3

And how do we do that?

Answer 4

just the normal process of evaluating limit. @jbn123

Answer 5

lim x->0 f(x)= lim x->0 (x^3+5)=5

Answer 6

limit at x=0 and f(0) must be equal for continuity

Answer 7

but f(0) and x=0 are the same thing? and since those both equal 5, it is continuous?

Answer 8

@Princer_Jones

Answer 9

f(0) and lim x->0 f(x) must be equal for continuity @jbn123

Answer 10

since we are given the value of f(x), we can evaluate lim x->0 f(x) and then for continuity, this computed value must be equal to f(0)

Answer 11

f(0) = 0^3+5=0
lim x->0 f(x) = 0^3 +5

Answer 12

so the computed value is equal

Answer 13

dont write f(0)=0^3+5 since the function is not yet defined . we need to define f(0) from the continuity part. @jbn123

Answer 14

That's the part i dont understand

Answer 15

@jbn123 check the attachment, i hope you understand this time

Answer 16

okay that makes sense

Answer 17

but what about one like this

Answer 18

@Princer_Jones

Answer 19

@jbn123 every function is not continuous .

Answer 20

But it says "in each case below define f(0) so that it BECOMES continuous" so surely ill have to define it at a point where it is continuous?

Answer 21

The last function is continuous only at x=0 if we define f(x)=0

Answer 22

that function is no where else continuous

Answer 23

I mean f(0)=0

Answer 24

OK here are the answers, for the 1st one, f(0)=1 and for the second one f(0)=0

Answer 25

I kinda need to understand why those are the answers. Would you mind explaining how you got to that?

Answer 26

yeah i told you take the limits when x tends to 0- and x tends to 0+ see that both will be same and for continuity, the limit value must be equal to the functional value