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

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

Grade:12th pass

1 Answers

Snehal Jadhav
54 Points
3 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
 

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