Single Choice x(1-acosx) - bsin x X...
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Single Choice x(1-acosx) - bsin x X=0 Let f(0)=1. The value of a and b so that fis a continuous function are: and A 5/2, 3/2 B 5/2, -3/2 C -5/2, -3/2 D None of these

JEE/Engineering Exams
Maths
Solution
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( f(x)=frac{x(1+a cos x)-b sin x}{x^{3}} ) ( f(0)=1 ) for ( (t+f(x)=f(0) ) ( x rightarrow 0 ) then, 51 is continew ( lim _{x rightarrow 0} f(x)=lim _{x rightarrow 0} frac{x(1+operatorname{acos} x)-operatorname{bsin} x}{x^{3}} rightarrow frac{0}{0} f(0) ) ( f(0)=lim _{x rightarrow 0} frac{(1+a cos x)+x(-a sin x)-b cos x}{3 x^{2}} ) ( f(0)=lim _{x rightarrow 0} frac{1+a cos x-a x sin x-b cos x}{3 x^{2}} ) When we substitute ( x=0 ), denominato" is "O" but numerator is ( 1+a-b ) So, for it to be confinows it should be ( i n frac{0}{0} operatorname{fog} m cdot 30, quad 1+a-b=0 rightarrow 0 )
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