1.

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?

Answer»

`lim_(theta to 0^(+)){(alpha(theta))^(1/(SINTHETA))+(beta(theta))^(1/(sintheta))}=1/(e^(2))`
`In (beta(theta))` is AODD `fn`
`lim_(theta to 0) (sum_(r=1)^(n) r^(1/(alpha^(2)(theta))))^(alpha^(2)(theta))=n, n epsilon N, h GE2`
`lim_(theta to pi//2)(alpha(theta)-(alpha(theta))^(alpha(theta)))/(1-alpha(theta)+In(alpha(theta)))=2`

Solution :`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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