Standarard limit sinx/x, tanx/x, 1-cosx/x^2 , e^x-1/x, a^x-1/x, n(1+x)/x based question

(x+sinx)/(1-cosx)

Find dy/dx when : y=x^(sinx-cosx)+(x^(2)-1)/(x^(2)+1)

If 0 lt x lt pi and cosx+sinx = (1)/(2) , then tanx is :

lim_(x rarr 0) (1+sinx-cosx+log_e(1-x))/x^2

If f(x)=[(sinx,cosecx,tanx),(secx,xsinx,xtanx),(x^2-1,cosx,x^2+1)] then int_(-a) ^ a f(x) dx equals

The limit of [(1)/(x^(2))+((2)^(x))/(e^(x)-1)-(1)/(e^(x)-1)] as x rarr0

The value of lim_(x->0)((sinx-tanx)^2-(1-cos2x)^4+x^5)/(7(tan^(- 1)x)^7+(sin^(- 1)x)^6+3sin^5x) equal to :

If f(x)=sinx+cosx, g(x)= x^(2)-1 , then g{f(x)} is invertible in the domain