The function f(x) = x sinx satisfies the following equation f”(x) + f(x) + t cosx = 0. The value of t is
(A) -1
(B) -2
(C) 1
(D) 2
Answer: (B)
Explanation:
We have f(x) = x sin x ⇒ f'(x) = x cos x + sin x ⇒ f′′(x) = x (− sin x ) + cos x + cos x = (−x sin x ) + 2 cos x Now, it is given that f(x) = x sin x satisfies the equation f′′(x) + f(x) + t cos x = 0 ⇒ (−x sin x ) + 2 cos x + x sin x + t cos x = 0 ⇒ 2 cos x + t cos x = 0 ⇒ cos x ( t + 2 ) = 0 ⇒ t + 2 = 0 ⇒ t = −2
Thus, B is the correct option.
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