CUET and UG exam TS EAMCET Engineering Mock Test Series 2025 Mathematics Limit and Continuity Continuity of a function
The values of a, b, c for which the function \(\rm f(x)=\left\{\begin{matrix}\frac{\sin (a+1)x+\sin x}{x},x<0\\\ c,x=0\\\ \frac{(x+bx^2)^{1/2}-x^{1/2}}{bx^{1/2}},x>0\end{matrix}\right.\) is continuous at x = 0, are
1
\(\rm a=\frac{3}{2}, b=-\frac{3}{2}, c=\frac{1}{2}\)
2
\(\rm a=-\frac{3}{2}, c=\frac{3}{2}\), b is arbitrary non-zero real number.
3
\(\rm a=-\frac{5}{2}, b=-\frac{3}{2}, c=\frac{3}{2}\)
4
a = -2, b ∈ ℝ - {0}, c = 0