Let `kgt0 and lambda =lim_(xrarr0) (k(1-4sqrt(k^2-x^2)))/(x^2sqrt(k^2-x^2))` be finite. Then the value of `lambdak`, isA. `lambda=8,k=(1)/(2)`B. `lambda=8,k=(1)/(4)`C. `lambda=4, k=(1)/(2)`D. `6lambda=4,k=(1)/(4)`

Let `kgt0 and lambda =lim_(xrarr0) (k(1-4sqrt(k^2-x^2)))/(x^2sqrt(k^2-

1.	Let `kgt0 and lambda =lim_(xrarr0) (k(1-4sqrt(k^2-x^2)))/(x^2sqrt(k^2-x^2))` be finite. Then the value of `lambdak`, isA. `lambda=8,k=(1)/(2)`B. `lambda=8,k=(1)/(4)`C. `lambda=4, k=(1)/(2)`D. `6lambda=4,k=(1)/(4)`
Answer» Correct Answer - B It is given that ` lambda =lim_(xto0) (k(1-4sqrt(k^2-x^2)))/(x^2sqrt(k^2-x^2)) "exists "` `rArrlim_(xto0)k(1-4sqrt(k^2-x^2))=0 rArr 1-4k=0rArr k=(1)/(4)` `therefore lambda =lim_(xto0) (1-sqrt(1-16x^2))/(x^2sqrt(1-16x^2))` ` rArr lambda =lim_(xto0)(1)/(x^2(1+sqrt(1-16x^2)sqrt(1-16x^2))` ` rArr lambda =16lim_(xto0)(1)/(x^2(1+sqrt(1-16x^2))sqrt(1-16x^2))` Hence ,`lambda =8 and k=(1)/(4)`

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