If logey=3sin−1x, then (1−x2)y′′−xy′ at x=21 is equal to
03Medium63×since 2002Q3684
Let f:(−∞,∞)−{0}→R be a differentiable function such that f^{\prime}(1)=\lim _\limits{a \rightarrow \infty} a^2 f\left(\frac{1}{a}\right). Then \lim _\limits{a \rightarrow \infty} \frac{a(a+1)}{2} \tan ^{-1}\left(\frac{1}{a}\right)+a^2-2 \log _e a is equal to
04Easy63×since 2002Q3685
If x=ey+ey+ey+.....∞ , x>0, then dxdy is
05Medium63×since 2002Q3686
If xm.yn=(x+y)m+n, then dxdy is
06Easy63×since 2002Q3687
If xlog_e(log_ex) − x² + y² = 4(y > 0), then dxdy at x = e is equal to :
07Easy63×since 2002Q3688
For x > 1, if (2x)^2y = 4e^2x−2y,
then (1 + log_e 2x)² dxdy is equal to :
08Easy63×since 2002Q3689
If cos−1(2y)=loge(5x)5,∣y∣<2, then :
09Easy63×since 2002Q3690
The value of loge2dxd(logcosxcosecx) at x=4π is