Find a and b so that the rational function f(x) = (ax^4 + bx^3 + 3) / (x^3 - 2) has an oblique asymptote given by y = x - 5.
+129849 f(x) = (ax^4 + bx^3 + 3) / ( x^3 -2)
We need to use long divsion
ax + b
x^3- 2 [ ax^4 + bx^3 + 0x^2 + 0x + 3 ]
ax^4 -2x
__________________________________
bx^3 2x
bx^3 -2b
___________________________
( 2x + 2b ) this remainder is ignored
So .....ax + b = x - 5
So
a =1 and b = -5
See the graph here : https://www.desmos.com/calculator/yi1t4tgsu5
