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

If lim_(xto0) (ae^(x)-b)/(x) =2, then find the values of a and b.

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

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

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

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

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 ("lim")_(xvec0)(cos4x+acos2x+b)/(x^4) is finite, find aa n db using expansion formula.

If lim_(xto2) (x^(n)-2^(n))/(x-2)=80" and " ninN, " then find the value of n."

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