Wednesday

April 16, 2014

April 16, 2014

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)

**Related Questions**

polynomials - (3+7x)-(16x2+15x2) (3+1x)-(12x+16+0+18x2) Q4: (15+13x2+14x2)+(13x...

polynomials - (3+7x)-(16x2+15x2) (3+1x)-(12x+16+0+18x2) Q4: (15+13x2+14x2)+(13x...

Math help please check - Add or Subtract for #3-4 3. (2x2 + 6x + 1) + (–7x2 + ...

math - If the value of x is 0, then what is the value of y in the function y = ...

Math: Check answers - 1. How can this product be simplified? 5x2(2x – 3) 5x2 + ...

calculus - f(x)=(9x^2–8)^6(4x^2–5)^11 Find f'(x) I got (9x^2-8)^6 *11(4x^2-3)^...

math - (5x2 + 9) + (7x2 + -8) = _____?

math - Use factoring by grouping to solve the following equation. 4x^3 + 8x^2 &#...

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

math - Solve the equation. (Enter solutions from smallest to largest. If there ...