Question

 is continuous at x = 0, then

Solution

Correct option is

A = – 4 & f(0) = 1

Let g(x) = sin 3x + A sin 2x + B sin x and  since g(0) = h(0) = 0.

  

Again  and  exists, so  

          3 + 2A + B = 0               … (i)  

In this case,

           

            

           

By similar argument,  

        27 + 8A + B = 0                … (ii)  

So the last limit is equal to  

          

         f (0), if f is continuous at x = 0. 

Solving (1) and (2), we get A = –4 and B = 5, so f(0) = 1

SIMILAR QUESTIONS

Q1

The number of points at which the function f(x) = 1/log |x| is discontinuous is

Q2

For  R, 

Q3

The value of a for which  tends to a finite limit as  is

Q4

Let 

where g is a continuous function. Then  exists if

Q5

The value of  is

Q6

Let Then the value of f (0) so that the function fis continuous is

Q10

Evaluate the right hand limit and left hand limit of the function