Question

The equation sin x + x cos x = 0 has at least one root in the interval

Solution

Correct option is

(0, π)

Consider the function given by,   

                 

We observe that                              f (0) = f (π) = 0    

∴ 0 and π are two roots of f (x) = 0.  

Consequently, f’(x) = 0 i.e., sin x + x cos x = 0   

has at least one root in (0, π).

SIMILAR QUESTIONS

Q1

If f (x) = xα log x and f (0) = 0, then the value of ‘α’ for which Rolle’s theorem can be applied in [0, 1] is:

Q2

If abc be non-zero real numbers such that  

                                                                      

Then the equation ax2 + bx + c = 0 will have

Q3

 

Find c of the Lagrange’s mean value theorem for which

Q4

Let f (x) and g (x) be differentiable for 0 ≤ x ≤ 2 such that (0) = 2, g(0) = 1 and f (2) = 8. Let there exists a real number c in [0, 2] such that f’(c) = 3g’(c) then the value of g(2) must be:

Q5

If f (x) = loge x and g(x) = x2 and c Ïµ (4, 5), then  is equal to: 

Q7

In [0, 1] lagrange’s mean value theorem is not applicable to

Q8

Let f (x) satisfy the requirement of lagrange’s mean value theorem in [0, 2]. If f (0) and   

 

Q9

Let f : [2, 7] and [0, ) be a continuous and differentiable function.

Then the value of (f (7) – f (2))  is (where c Ïµ (2, 7))

Q10

Let f (x) = ax5 + bx4 + cx3 + dx2 + ex, where abcde Ïµ R and f (x) = 0 has a positive root α, then