(a) {(ax +1 , x ≤ 3)(bx + 3, x > 3) is continuous. if bx + 3 x > 3

Question

\((a) \begin{cases} ax +1 & x ≤ 3\\\ a \times bx + 3, & x>3 \end{cases} \) is continuous if bx + 3. x>3

(b) If e^y (x + 1) = 1, show that \(\frac{d^2y}{dx^2} = (\frac{dy}{dx})^2\)

Answer 1

(a) f is continuous at x = 3 

(b) Given; e^y (x+1) =1

Differentiating w.r.t to x, we get;