Question

will medal and fan

Answer 1

prove that the function f(x)=xsin1/x, \[x \neq 0 , and f(0)=0\] is continuous but not derivable at the origin

Answer 2

to prove continuity evaluate the limit of f(x) at 0
if it is zero then the function is continuos

Answer 3

the second part there is a differentiability problem at zero
take the definition of derivative to arrive at two different values for the limit from the right and from the left

Answer 4

got the first one but the second is difficult for me. please can you help me evaluating it

Answer 5

\[\rm f'(x)=\lim_{x\to 0}\frac{f(x)-f(0)}{x}=\lim_{x\to 0}\frac{x\sin \frac{1}{x}}{x}=\]

Answer 6

cancel x since x does not equal zero
left with lim sin(1/x)
which the same as \[\lim_{x \to \infty}\sin x=(-1)^n\]

Answer 7

so the limit does not exist therefore the function is not differentiable at 0

Answer 8

got it?

Answer 9

very cool, thanks . i have about 3 more similar questions . should i post?

Answer 10

yw! let's see, i have very little time though
i need to go bad to my books lol

Answer 11

thanks.

Answer 12

show that f(x)\[\left| x \right| + \left| x-1 \right|\] is continuous but not derivable at x=0 and x=1

Answer 13

hmm you are going at the same way

Answer 14

let me see you do the continuity

Answer 15

how do we verify if f is continuous at 0?

Answer 16

are you speechless, talk with me, you know it is not interesting at all if you just stay calm on the screen

Answer 17

alright times out i wanted to help but you are not putting efforts

Answer 18

sorry. went to pee

Answer 19

you there?

Answer 20

thanks for coming back

Answer 21

i only know that a function is continuous if it posses a differential co-efficient but don't really know how to prove it

Answer 22

hmm not even sure what you mean lol, enlight me on how to do it with that way
\[\rm f~is~continuous~at~x=c~iff~ \lim_{x\to c}f(x)=f(c) \]
this the theorem i know of

Answer 23

what i do know is that f is differentiable implies f continuous
what do you mean by coefficient thingy?

Answer 24

yes

Answer 25

that is what i meant

Answer 26

sir you there?

Answer 27

yes

Answer 28

does it mean that tha f(x) will be 2x-1?

Answer 29

find f(0)
evaluate lim f(x) at 0 to see if they are euql

Answer 30

equal

Answer 31

f(0)=2(0)-1=-1
am i correct?

Answer 32

where is absolute values?
you have |x|+|x-1| no?

Answer 33

should be 1 not -1

Answer 34

do the limit

Answer 35

f(x)=2x+1
f(0)=2(0)+1=1

Answer 36

correct?

Answer 37

why did you make f(x)=2x+1?
our function is \[f(x)=|x|+|x-1|\]

Answer 38

gotta go buddy
need to go sleep sorry

Answer 39

please am lost here

Answer 40

i really need to go sleep have an exam tomorrow, sorry!

Answer 41

it is too late here

Answer 42

ok. thanks for the help so far. can you tell me when you be online again?