InterviewSolution
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InterviewSolution
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If`("lim")_(xvec0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0,s mftheta in (-pi,pi],`then the value of `theta`is`+-pi/4`(b) `+-pi/3`(c) `+-pi/6`(d) `+-pi/2`A. `+-(pi)/(4)`B. `+-(pi)/(3)`C. `+-(pi)/(6)`D. `+-(pi)/(2)` |
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Answer» Correct Answer - D We have, `lim_(xto0) {1+x In (1+b^2)}^(1//x)=2bsin^2theta` `rArr e^(lim_(xto0)xIn (1+b^2)xx(1)/(x))=2bsin^2theta ` `rArr ^In (1+b^2=2bsin^2theta` `rArr 1+b^2=2bsin^2theta` `rArr sin^2theta (1+b^2)/(2b)` `rArr sin^2theta=(1)/(2)(b+(1)/(b))[because b+(1)/(b)ge 2therefore(1)/(2))ge 1]` `rArr sin^2theta=1` `rArr theta=+-(pi)/(2)`. |
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