0

Guest

Courses New

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?

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?

Grade:9

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 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

Think You Can Provide A Better Answer ?

Other Related Questions on Differential Calculus

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More