Flag Differential Calculus> Can we say that all even functions are co...
question mark

Can we say that all even functions are continuous and non differentiable at x=0 and all odd functions are continuous and differentiable at x=0?

Leo Pixie , 10 Years ago
Grade 9
anser 1 Answers
Jitender Singh

Last Activity: 10 Years ago

Ans: No
Odd Function:
f(x) = \frac{1}{x}
Limitat x =0 does not exist. So f(x) is neither continuous nor differentiable at zero.
\lim_{h\rightarrow 0^{+}}\frac{1}{x} = \infty
\lim_{h\rightarrow 0^{-}}\frac{1}{x} = -\infty
Even Function:
f(x) = x^{2}
To check continuity
\lim_{h\rightarrow 0^{+}}h^{2} = 0
\lim_{h\rightarrow 0^{-}}h^{2} = 0
To check differentiability
RHD = \lim_{h\rightarrow 0}\frac{h^{2}-0}{h} = \lim_{h\rightarrow 0}h = 0
LHD = \lim_{h\rightarrow 0}\frac{(-h)^{2}-0}{-h} = \lim_{h\rightarrow 0}(-h) = 0
So f(x) is continuous & differentiable at zero.
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

Provide a better Answer & Earn Cool Goodies

Enter text here...
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Enter text here...