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If `alpha(theta) epsilon R` & `beta(theta),theta epsilon R-{2n pi-(pi)/2, n epsilin I}` are functions satistying `(1+x)sin^(2)theta-(1+x^(2))sintheta +(x-x^(2))=0` then which of the following is/are correct?A. `lim_(theta to 0^(+)){(alpha(theta))^(1/(sintheta))+(beta(theta))^(1/(sintheta))}=1/(e^(2))`B. `In (beta(theta))` is a odd `fn`C. `lim_(theta to 0) (sum_(r=1)^(n) r^(1/(alpha^(2)(theta))))^(alpha^(2)(theta))=n, n epsilon N, h ge2`D. `lim_(theta to pi//2)(alpha(theta)-(alpha(theta))^(alpha(theta)))/(1-alpha(theta)+In(alpha(theta)))=2` |
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Answer» Correct Answer - A::B::C::D `x^(2)-((1+sin^(2)theta)/(1+sintheta))+((sintheta-sin^(2)theta)/(1+sintheta))=0` `x^(2)-x(sintheta+(1-sintheta)/(1+sintheta))+sintheta((1-sintheta)/(1+sintheta))=0` `impliesx=sintheta , (1-sintheta)/(1+sintheta)` `impliesalpha(theta)=sintheta, beta(theta)=(1-sintheta)/(1+sintheta)` Hence the results follows. |
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