I have a whole packet on continuity and i dont understand it at all. I have tried using my book but im at a loss. I have two questions one involving infinity.
(6x-18)/(x^4-14x^3+49x^2) or 6x - 18 all over x to the 4th - 14x cubed + 49x squared
Find each point of discontinuity of f and for each give the value of the point of discontinuity and evaluate the indicated one-sided limits.
Evaluate the following limits
lim as x approaches infinity (11-x)(9+7x) all over (3-8x)(5+10x)
lim as x approaches negative infinity (11-x)(9+7x) all over (3-8x)(5+10x)
please anyone who can help im not looking for the answers just a better understanding of how to solve for continuity.
A function written as f(x)/g(x) where both f(x) and g(x) are polynomials is discontinuous only at the points where g(x) = 0. So for the first question, you would solve for the denominator being equal to 0. It is clearly equal to 0 when x = 0, because you can factor out an x^2. To find the other points where it is equal to 0, solve the resulting quadratic equation.
Ok so that makes since, where would dividing but the highest common value of x come into play?