Question

Please help with the continuity question:--

Answer 1

What is your question?

Answer 2

\[f(x)=|x-a| \phi(x)\],where \[\phi(x) \] is a continuous function.Then which of the following holds true:-

Answer 3

(a.)\[f'(a^+)=\phi (a)\]
(b).\[f'(a^-)=-\phi(a)\]
(c.)\[f'(a^+)=f'(a^-)\]
(d).none of these.

Answer 4

please help!

Answer 5

Do you know the condition for continuity @maheshmeghwal9 ??

Answer 6

ya!

Answer 7

Make sure you write
f(x) = (x-a)ϕ(x) for x>=a
= -(x-a)ϕ(x) for x<a

Then differentiate f(x) for case (1)-->x>=a
case(2)---> x<a

And then finally after differentiate, put x=a and check your options

Answer 8

will i get the answers ?

Answer 9

I got the answer. So you should get it too :)

Answer 10

what do u get? a or b or c or d.

Answer 11

Wait. Let me verify whether the other options are wrong before telling you the answer

Answer 12

k:) I try ur method also

Answer 13

The answer is a)

Answer 14

but the ans...s are A & B.

Answer 15

Yes. Yes. :)

Answer 16

I thought it was single choice answer and wondering .. :P

Answer 17

k! np:) now wait please I try also

Answer 18

but how I differentiate

Answer 19

please tell:)

Answer 20

For case 1
Take
u = x-a
v = ϕ(x)
\[\frac{d}{dx}(uv) = u'v +uv'\]

where
\[u' = \frac{d}{dx}(u)\]
\[v'=\frac{d}{dx}(v)\]

Hopefully you know to differentiate know :0

Answer 21

k!will i get 1 after differentiating x-a as u?

Answer 22

No boss
Looks like you are really confused. Let me do case 1 for you. You do case 2 .

\[\frac{d}{dx} ((x-a)(ϕ(x)) = (\frac{d}{dx}(x-a))(ϕ(x))+(x-a)(\frac{d}{dx} (ϕ(x))\]
Now
\frac{d}{dx}(x-a) = 1
\frac{d}{dx}(ϕ(x)) = ϕ'(x)

Substituting this, we get
\[f'(x)=\frac{d}{dx} ((x-a)(ϕ(x)) = ϕ(x)+(x-a)((ϕ'(x))\]
Now
\[f'(a)= ϕ(a)+0= ϕ(a)\]

Similarly try case 2:

Answer 23

k! thanx a lot. I will do it now