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____`

If ("lim")_(xvec0)(a e^x-b)/x = 2 , then find the value of aa n dbdot

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

If ("lim")_(xveca)[f(x)+g(x)]=2a n d ("lim")_(xveca)[f(x)-g(x)]=1, then find the value of ("lim")_(xveca)f(x)g(x)dot

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

Evaluate ("lim")_(xvec0) (sinx-2)/(cosx-1)

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

("lim")_(xvec0)((1+5x^2)/(1+3x^2))^1//x^2=____

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

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

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)