find the limits of the following functions

Question

Limit x--> infinity 14+(4x/x^2-5x+6)

 

Limit x--> Infinity √(x^2+4x-8)-x

 

Limit x---> -Infinity √(x^2+4x-8)+x

Answer 1

Hi Lucy

 

See below.

 

Limit x--> infinity 14+(4x/x^2-5x+6) = 14+6+lim x->inf (4/x -5x) = 20+4/inf-5*inf = 20+0-inf = -inf

Limit x--> Infinity √(x^2+4x-8)-x = {let's call the root expression z for now so I have to type less} =

 

lim [z-x] = lim [z(1-x/z)] - lim [(1-x/z)/(1/z)]

Now apply L'Hospital's rule (differentiate) and ... you get ... lim [2(x-4)/(x+2)]

Apply L'Hospiatl's rule again, and you get lim [2(1)/(1)] = lim x->inf [2] = 2

Limit x---> -Infinity √(x^2+4x-8)+x

Use the same approach as in the 2nd problem.

 

Cheers,

Alex