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NDA Math Limit, Continuity and Differentiability

For the next three (03) items that follow:

Let f(x) be a function in

1\le x < \infty

f(x)=\begin{cases} 2-x & \text{for } 1\le x\le 2 \\ 3x-x^2 & \text{for } x>2 \end{cases}

[NDA I 2014]

Question : 99 of 105

Marks: +1, -0

[1,\infty)

x=1.5

Solution:

L.H.L=\lim\limits_{x\to2^{-}}f(x)=0

R.H.L=\lim\limits_{x\to2^{+}}f(x)=2

L.H.L\neq R.H.L

f(x)

not differentiable at

x=2

, therefore not continuous

For

x<2,\ f(x)=2-x

is a linear function which is always continuous and differentiable.

For

x>2,\ f(x)=3x-x^2

is a quadratic function which is always continuous and differential

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