Determine the real numbers and so that the function h(x)= cases a x^ 2 +3, & x<1

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

Problem

Determine the real numbers

a

and

b

so that the function

h(x)= \begin{cases} a x^{2}+3, & x<1,\\ a + b x, & 1\le x <3,\\ \ln x + b, & x\ge 3 \end{cases}

is continuous for all real

x