If `3-((x^2)/(12))lt=f(x)lt=3+((x^3)/9)` for all `x!=0,` then find the value of `("lim")_(xvec0)f(x)`

If (x^2+x−2)/(x+3) 1) f(x) then find the value of lim_(x->1) f(x)

Evaluate: ("lim")_(xvec0)(1-cos2x)/(x^2)

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

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of (lim)_(xvec0)(((dy)/(dz)))/x

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

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

Evaluate: ("lim")_(xvec0)(cot2x-cos e c2x)/x

If f(x) is differentiable and strictly increasing function, then the value of ("lim")_(xvec0)(f(x^2)-f(x))/(f(x)-f(0)) is 1 (b) 0 (c) -1 (d) 2

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