Find `("lim")_(xvec0){tan(pi/4+x)}^(1//x)`

Evaluate the limit: ("lim")_(xvec0)(sina x)/(sinb x)

The value of the limit ("lim")_(xvec0)(a^(sqrt(x))-a^(1 / sqrt(x)))/(a^(sqrt(x))+a^(1 / sqrt(x))),a >1,i s 4 (b) 2 (c) -1 (d) 0

f(x) is polynomial function of degree 6, which satisfies ("lim")_(xvec0)(1+(f(x))/(x^3))^(1/x)=e^2 and has local maximum at x=1 and local minimum at x=0a n dx=2. Column I, Column II The coefficient of x^6 , p. 0 The coefficient of x^5 , q. 2 The coefficient of x^4 , r. -(12)/5 The coefficient of x^3 , s. 2/3

Evaluate: ("lim")_(xvec0)(sin^(-1)x-tan^(-1)x)/(x^3)

If ("lim")_(xvec0)[1+x+(f(x))/x]^(1/x)=e^3, then find the value of 1n(("lim")_(xvec0)[1+(f(x))/x]^(1/x))i s____

f(x)={x ,xlt=0 1,x=0,then find ("lim")_(xvec0) f(x) if exists x^2,x >0

Consider P(x) to be a polynomial of degree 5 having extremum at x=-1,1, and ("lim")_(xvec0)((p(x))/(x^3)-2)=4 . Then the value of [P(1)] is (where [.] represents greatest integer function)___

If m , n in N ,("lim")_(xvec0)(sinx^m)/((sinx)^m)i s 1,ifn=m (b) 0,ifn > m oo,ifn

Evaluate: ("lim")_(xvec0)(1+x)^(os e cx c)

Evaluate: ("lim")_(xvec0)(1-cosm x)/(1-cosn x)