displaystyle limx → y ((xy-yx/xx-yy)), is equal to

Question

displaystyle limx → y ((xy-yx/xx-yy)), is equal to (A) (1+log y/log y) (B) (1-log y/1+log y) (C) (1-log y/log(ey)) (D) log (ex)

Tardigrade Admin · Accepted Answer

displaystyle limx → y ((xy-yx/xx-yy)) ((0/0) form) Using Lâ Hospital Rule, we get displaystyle limx → y (yxy-1-yx log y/xx log(ex)) =(1-log y/log(ey))

Q. $x \to y lim$ $(\frac{x ^{y} - y ^{x}}{x ^{x} - y ^{y}})$ , is equal to

$\frac{1 + l o g y}{l o g y}$

$\frac{1 - l o g y}{1 + l o g y}$

$\frac{1 - l o g y}{l o g ( ey )}$

$l o g (e x)$

$x \to y lim$ $(\frac{x ^{y} - y ^{x}}{x ^{x} - y ^{y}})$ $(\frac{0}{0}$ form $)$
Using $L ’$ Hospital Rule, we get
$x \to y lim$ $\frac{y x ^{y - 1} - y ^{x} l o g y}{x ^{x} l o g ( e x )}$
$= \frac{1 - l o g y}{l o g ( ey )}$

Q. x→ylim​ (xx−yyxy−yx​), is equal to

logy1+logy​

1+logy1−logy​

log(ey)1−logy​

log(ex)