Thursday

August 28, 2014

August 28, 2014

Posted by **Jin** on Saturday, September 4, 2010 at 12:18am.

Find the equation of the non-vertical asymptote.

y =

Does f(x) intersect its non-vertical asymptote? (yes or no)

What is the smallest value of x at which f(x) intersects its non-vertical asymptote? ( Enter No in the question blank if you answered no above.) .

- calculus -
**MathMate**, Saturday, September 4, 2010 at 7:53amThe equation of the non-vertical asymptote can be found by evaluating

Lim x→±∞ f(x)

The limit can be found by dividing both the numerator and denominator by x² and is found to be -(8/7)x.

Thus the equation of the non-vertical asymptote is

y=-(8/7)x ....(1)

To find out if f(x) intersects (1) above, we equate

f(x)=-(8/7)x .....(2)

and solve for x.

Since the x³ terms cancel, (2) reduces to a quadratic with roots at

x=(3*√(46)+8)/25, or

-(3*√(46)-8)/25

Make your pick for the leftmost intersection point.

Check my work.

**Related Questions**

CALCULUS HELP ! - f(x)=(-3x^3-x^2-9x-8)/(6x^2+4x+3. Find the equation of the non...

CALC - f(x)=x^3-3x^2-3x-8/(-3x^2-4x-6) Find the equation of the non-vertical ...

Calculus - f(x)= (-5x^3 + 3x^2 + 3x -5)/(-8x^2 +2x + 7) Find the equation of the...

CALCULUS! - f(x)=(6x^3–9x^2–3x–1)/(4x^2+7x–3) . Find the equation of the non-...

calc - f(x)=[5x^3-4x^2-8x+9]/[2x^2-1x-3] Find the equation of the non-vertical ...

calc - f(x)=[5x^3-4x^2-8x+9]/[2x^2-1x-3] Find the equation of the non-vertical ...

Math - Calculus - Find the equation of the non-vertical asymptote. What is the ...

calculus - Find the equation of the non-vertical asymptote. y=?? 5x^3+5x^2+8x-7...

CALC 2a - f(x)=x^3-3x^2-3x-8/(-3x^2-4x-6) Find the equation of the non-vertical...

Calc - f(x)=x^3-3x^2-3x-8/(-3x^2-4x-6) Find the equation of the non-vertical ...