If `(x)/(x-1)+(x-1)/(x)>0` then x is

If (x+1)(x+2)+1/(x(x-1))=0 then find x^2+x

If f(x)= {(([x]-1)/(x-1), x ne 1),(0, x=1):} then f(x) is

Is f(x)=(1+x)^((1)/(x)), when x!=0=e, when x=0 continuous at x=0?

If y = Cos^(-1){(x-x^(-1))/((x+x^(-1))} , x>0 then find dy/dx

If lim_(x rarr0)[1+x+(f(x))/(x)]^((1)/(x))=e^(3), then the value of ln(lim_(x rarr0)[1+(f(x))/(x)]^((1)/(x))) is

If lim_(x rarr0)(a^(sin x)-1)/(1+x-cos x)=lim_(x rarr1)(x-1)/(ln(x)) then a=

f(x)={sqrt(x)(1+x sin((1)/(x))),x>0;-sqrt(-x)(1+x sin((1)/(x))),x<0;0,x, then f(x) is

If f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne 0),(0 , x =0 ):} then f(x) is

If f(x)={{:(x^(p+1)cos.(1)/(x)":", x ne 0),(0":", x=0):} then at x = 0 the function f(x) is