Question

Identify the horizontal asymptote of f(x) = (x^2+5x-3)/(4x-1)

Answer 1

set the denominator equal to zero and solve
i.e. solve for \(x\) : \(4x-1=0\)

Answer 2

won't it be vertical asymptote?

Answer 3

horizontals are for large values of x

Answer 4

for large values of x; this is practically the same as x^2/4x

Answer 5

vertical asymptote at x = 1/4?

Answer 6

x/4 + 21/16
--------------
4x-1 | x^2+5x-3
-(x^2-x/4)
-----------
21/4 x - 3
- (21/4x - 21/16)
-----------------
R

the limit as x appraoches infinity, the remainder goes to zero and we are left with

ha = \(\frac{1}{16} (4x + 21)\)

if im remembering it correctly

Answer 7

err, thats the slant asymptote; there is non horizontal that i can tell