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# is Continuous At x = 0, Then

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## Question

### 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