1.

Sigma_(r=1)^(oo) 3^(r-1)(sin.(theta)/(3^(r)))^(3)is equal to

Answer»

`theta - sin theta`
`(1)/(2)(theta-sintheta)`
`sin theta-theta`
`(1)/(4)(theta-sintheta)`

Solution :`((y-x)/(tan^(-1)y-tan^(-1)x))=(1)/(m)`
`A(x, tan^(-1)x)`
`B(y,tan^(-1)y)`
`m="Slope of" AB =((tan^(-1)y-tan^(-1)x)/(y-x))`
'm' is minimum as A, Bboth tend to POINT with x-coordinate `(SQRT(3))`
`implies m gt (d)/(dx) (tan^(-1)x)|_(x=sqrt(3))`
`implies m gt ((1)/(1+x^(2)))|implies MGT(1)/(4)`
`(1)/(m)lt4implies "MAXIMUM integral value of"((1)/(m)) "is" 3`.


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