Define f(x)= cases (bx) x , & x<0

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Define

f(x)=\begin{cases} \dfrac{\sin(bx)}{x}, & x<0,\\ a x^{2}+b, & 0\le x<2,\\ \sqrt{x+ab}, & x\ge 2. \end{cases}

Determine all real numbers

a

and

b

for which

f

is continuous on the entire real line.

Related theory

Browse the problem library