Question

The number of points in (-∞, ∞) for which x2 – x sin x – cos x = 0 is

(a) 6

(b) 4

(c) 2

(d) 0

 

 

Answer 1

Let f(x) = x² – x sin x – cos x = 0

f’(x) = 2x – sin x – x cos x + sin x

=> 2x – x cos x = 0

When x> 0, f(x) is increasing.

When x< 0, f(x) is decreasing.

f(0) = -1

f(∞) = ∞

f(-∞) = ∞

lim x→ +∞f(x) = ∞

lim x→ -∞f(x) = ∞

Using the intermediate value theorem, it will cut the x-axis at 2 points.

Thus 2 solutions.

 

 

The number of points are 2.