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" (i) "(1+x^(2))/(sqrt(x))...

" (i) "(1+x^(2))/(sqrt(x))

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int(1-x^(2))sqrt(x)dx

if tan^(-1){(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))}=alpha then

if tan^(-1){(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))}=alpha then

Show that : Lt_(x to 0)(sqrt(1+x)-sqrt(1+x^(2)))/(sqrt(1+x^(2))-sqrt(1-x))=1

int(sqrt(1-x^(2))+sqrt(1+x^(2)))/(sqrt(1-x^(2))sqrt(1+x^(2)))dx=

underset(x to 0)"Lt" (sqrt(1-x)-sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1+x))=

tan^(-1)[(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))],|x|<(1)/(2),x!=0

y=tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))), where -1