R D Sharma Solutions for Chapter: Continuity, Exercise 1: EXERCISE

Determine the value of the constant $k$ so that the function

$f\left(x\right)=\left\{\begin{array}{cc}\frac{\sin 2x}{5x}& , \text{if} x\ne 0\\ k& , \text{if} x=0\end{array}\right.$ is continuous at $x=0$.

Find the values of $a$ so that the function $f\left(x\right)=\left\{\begin{array}{cl}ax+5& , \text{if} x\le 2\\ x-1& , \text{if} x>2\end{array}\right.$ is continuous at $x=2$.

Find the value of the constant $k$ so that the given function is continuous at the indicated point; $f\left(x\right)=\left\{\begin{array}{l}kx+1 \text{if} x\le 5\\ 3x-5, \text{if} x>5\end{array}\right.$ at$x= 5$.

Find the value of the constant $k$ so that the given function is continuous at the indicated point; $f\left(x\right)=\left\{\begin{array}{l}\frac{x^2-25}{x-5}, x\ne 5\\ k , x=5\end{array}\right.$ at $x= 5$.

Find the value of the constant $k$ so that the given function is continuous at the indicated point; $f\left(x\right)=\left\{\begin{array}{ll}k{x}^2,& x\ge 1\\ 4& , x<1\end{array}\right.$at $x=1$.

Find the value of the constant $k$ so that the given function is continuous at the indicated point; $f\left(x\right)=\left\{\begin{array}{ll}k\left(x^2+2\right),& \text{if} x\le 0\\ 3x+1& ,\text{if} x>0\end{array}\right.$ at $x=0$.

Find the value of the constant $k$ so that the given function is continuous at the indicated point; $f\left(x\right)=\left\{\begin{array}{ll}\frac{x^3+x^2-16x+20}{(x-2{)}^2},& x\ne 2\\ k, x=2& \end{array}\right.$ at $x=2$.

If the function $f\left(x\right)$, defined below is continuous at $x= 0$, find the value of $k$, where $f\left(x\right)=\left\{\begin{array}{l} \frac{1-\cos 2x}{2x^2} , x<0\\ k , x=0\\ \frac{x}{\left|x\right|} , x>0\end{array}\right.$.