Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Evaluate the following:

`tan^-1(-1/sqrt3)+cot^-1(1/sqrt3)+tan^-1(sin(-pi/2))`

Test the continuity of the function on f(x) at the origin: 

\[f\left( x \right) = \begin{cases}\frac{x}{\left| x \right|}, & x \neq 0 \\ 1 , & x = 0\end{cases}\] 

Prove that the function 

For what value of λ is the function 
\[f\left( x \right) = \begin{cases}\lambda( x^2 - 2x), & \text{ if }  x \leq 0 \\ 4x + 1 , & \text{  if } x > 0\end{cases}\]continuous at x = 0? What about continuity at x = ± 1?

Find the relationship between 'a' and 'b' so that the function 'f' defined by 

Find the points of discontinuity, if any, of the following functions: 

Find the points of discontinuity, if any, of the following functions: \[f\left( x \right) = \begin{cases}2x , & \text{ if }  & x < 0 \\ 0 , & \text{ if }  & 0 \leq x \leq 1 \\ 4x , & \text{ if }  & x > 1\end{cases}\]

Find the points of discontinuity, if any, of the following functions: \[f\left( x \right) = \begin{cases}x^{10} - 1, & \text{ if }  x \leq 1 \\ x^2 , & \text{ if } x > 1\end{cases}\]

Find the points of discontinuity, if any, of the following functions:  \[f\left( x \right) = \begin{cases}- 2 , & \text{ if }& x \leq - 1 \\ 2x , & \text{ if } & - 1 < x < 1 \\ 2 , & \text{ if }  & x \geq 1\end{cases}\]

In the following, determine the value of constant involved in the definition so that the given function is continuou: 

The function f (x) = tan x is discontinuous on the set