Please help me!!Find an equation of the slant asymptote. Do not sketch the curve.?
1. y = (x^2 + 2) / (x + 2)
2. y = (4x^3 - 2x^2 + 1) / (2x^2 + x - 4)
Solution
let y = mx+c be the asymptote
=>
y = mx+c, y = (x^2+2)/(x+2) should not have a solution for y =mx+c to be a asymptote
=>
mx+c = (x^2+2)/(x+2) have no solution
=>
(mx+c)(x+2) = x^2 +2 have no solution
=>
m = 1
=>c = -2
=>
y = x-2 is the assymptotes
2)
y = mx+c be an asymptote
=>
y = mx+c, y = (4x^3-2x^2 +1)/(2x^2+x-4) should not have a solution for y =mx+c to be a
asymptote
=>
mx+c = (4x^3-2x^2 +1)/(2x^2+x-4) have no solution
=>
(mx+c)(2x^2+x-4) = (4x^3 -2x^2+1)
=>
m = 2, c = -2
=>
y = 2x-2 is the asymptote.
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Please help me!!Find an equation of the slant asymptote. Do not sket.pdf
1. Please help me!!Find an equation of the slant asymptote. Do not sketch the curve.?
1. y = (x^2 + 2) / (x + 2)
2. y = (4x^3 - 2x^2 + 1) / (2x^2 + x - 4)
Solution
let y = mx+c be the asymptote
=>
y = mx+c, y = (x^2+2)/(x+2) should not have a solution for y =mx+c to be a asymptote
=>
mx+c = (x^2+2)/(x+2) have no solution
=>
(mx+c)(x+2) = x^2 +2 have no solution
=>
m = 1
=>c = -2
=>
y = x-2 is the assymptotes
2)
y = mx+c be an asymptote
=>
y = mx+c, y = (4x^3-2x^2 +1)/(2x^2+x-4) should not have a solution for y =mx+c to be a
asymptote
=>
mx+c = (4x^3-2x^2 +1)/(2x^2+x-4) have no solution
=>
(mx+c)(2x^2+x-4) = (4x^3 -2x^2+1)
=>
m = 2, c = -2
=>
y = 2x-2 is the asymptote
