If `("lim")_(xvecoo){(x^2+1)/(x+1)-(a x+b)}=0,` then find the value of `aa n dbdot`

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

If L=("lim")_(xvecoo){x-x^2(log)_e(1+1/x)}, then the value of 8L is_____

If lim_(xto0) (1+ax+bx^(2))^(2//x)=e^(3) , then find the values of a and b.

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

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_(n->oo)1/((sin^(-1)x)^("n")+1)=1 ,t h e n find the value of x.

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

If lim_(xtoa)(a^(x)-x^(a))/(x^(x)-a^(a))=-1" and "agt0," then find the value of a."

If equations x^2+a x+12=0. x^2+b x+15=0a n dx^2+(a+b)x+36=0, have a common positive root, then find the values of aa n dbdot

If the curve y=a x^2-6x+b pass through (0,2) and has its tangent parallel to the x-axis at x=3/2, then find the values of aa n dbdot