Sunday

March 1, 2015

March 1, 2015

Posted by **HELP!!! DESPERATE D;** on Friday, June 1, 2012 at 4:56am.

What is the smallest value of x at which f(x) intersects its non-vertical asymptote?

- Calculus -
**MathMate**, Friday, June 1, 2012 at 8:06amFirst we calculate the non-vertical (slant) asymptote as the leading term in the quotient represented by f(x), that is:

(-9x3–5x2+4x–2)/(–7x2–9x+7)

=9x/7 + .....

So g(x)=9x/7 is the non-vertical asymptote.

To solve f(x)=g(x), we can set

h(x)=f(x)-g(x)=0 and solve for x.

Thus,

h(x)=(-9x3–5x2+4x–2)/(–7x2–9x+7)-9x/7

we need to take the common denominator of 49*x^2+63*x-49 and add the two terms together to get:

h(x)=(-(46*x^2-35*x-14))/(49*x^2+63*x-49)

h(x) will vanish if and only if the numerator vanishes, which is the condition:

n(x)=-(46*x^2-35*x-14)=0

You only need to solve the quadratic equation n(x)=0 and select the smaller root.

Note: you need to check that the denominator of h(x) does not vanish at the same point!

-(46*x^2-35*x-14)

**Answer this Question**

**Related Questions**

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

calculus - f(x)=8x^3+1x^2–8x+2/–7x^2–4x+9 Find the equation of the non-vertical...

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

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

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

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 ...

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