Continuity and Differentiability

2. Given, f (x) = 2x2 1

At x = 3

Lim f (x) = $\frac{dy}{dx}=\frac{-\left(3x^2+2xy+y^2\right)}{\left(x^2+2xy+3y^2\right).}$ 2 (3)2 1 = 18 1 = 17.

So, f is continuous at x = 3.

1. Given, f (x) = 5x 3

At x = 0,  $\underset{x\to 0}{lim}f(x)=\underset{x\to 0}{lim}$ 5x 3 = 5 0 3 = 3.

So f is continuous at x = 1.

At x = 3,  $\pi +h$ 5x 3 = 5 ( 3) 3 = 15 3

= 18.

So f is continuous at x = 3.

At x = 5,  $\forall x\in ?$ .5x 3 = 5.5 3 = 25 3 = 22.

So, f is continuous at x = 5.