# Lim x tends to 0 sin2x+asinx/x³ be finit then the value of a and the limit are given by

54 Points
4 years ago
The condition for the given limit x tends to zero is that the expression should have finite value.
The common x tends to zero formulas are:
$\lim_{x\rightarrow 0}$ $\sin x$ / $x$ =1.....................(1)

$\lim_{x\rightarrow 0}$ (1 – $\cos x$)/ $x^{2}$ = 0.5.......(2)
The equation is:
(sin 2x + asin x)/x3

(2(sin x)(cos x) + asin x)/ x

sinx (2(cos x) + a)/x3

[(sin x)/x] * [(2(cos x) + a)/x2]
From, equation (2), a should be equal to [– 2] then:
The limit will be [(sin x)/x] * [(2(cos x) – 2)/x2]

= [1]*[(-)0.5*2]

= (–)1