Class 12

Math

Calculus

Continuity and Differentiability

For what value of $λ$is the function defined by $f(x)={λ(x_{2}−2x)4x+1 ifx≤0ifx>0 $ continuous at $x=0$? What about continuity at $x=1$?

$f(0_{−})=f(0_{+})$

$⇒λ(0−0)=4(0)+1$

$0=1,$ which is not true.

So, $f(x)$ is not continuots at $x=0$.

Now, at $x=1$,

Therefore, $f(x)$ is continuous at $x=1$.