Question

can i get some help with limits?

Answer 1

Almost certainly. What kind of limits do you need help with?

Answer 2

i have to show that f(x) has a removable discontiunty at x=2 and for what value of f(2) f(x) countionous. the equation is \[(2x^2+3x-14)/(x-2)\]

Answer 3

check to see if 2 makes the numerator zero. if it does factor and cancel

Answer 4

you get
\[(x-2)(2x+7)\] canceling gives you
\[2x+7\] replace x by 2 and get 11

Answer 5

i don't really get continuity at all i guess

Answer 6

ok the algebra is easy enough yes? so now the question is, what is the difference between
\[f(x)=\frac{2x^2+3x-14}{x-2}\] and
\[g(x)=2x+7\]which is just a line

Answer 7

You can only factor and cancel here because the denominator is equal to 0 at x=2. It's a little trick that follows from some theorems learned in pre-calc or calc 1.

To show it has removable discontinuity at x=2, you only have to say that the only place the function is undefined, is at x=2 (obvious since you can't divide by 0), and show that a limit exists at x=2.

To show the limit exists, you can check if the numerator, as well as the denominator is equal to 0 at x=2. If this is true, factor, cancel, and solve. Remember, this only works if the numerator AND the denominator are equal to 0.

Answer 8

and the answer is that they are identical, except for the fact that f is not defined at 2, but g is

Answer 9

so the graph of f looks just like the graph of g, a line with slope 2 and y intercept 7, except that at (2,11) where the function ought to be 11 there is a hole. other than that, they are identical

Answer 10

meaning that if you define f to be 11 when x = 2 now it is in fact identical to the line
\[y=2x+7\] and you have "removed" the discontinuity

Answer 11

sorry it took me so long respond, this online work is being very slow... anyway say i have 2 equations \[(4x^3+24x^2+7x+42)/(x+6) and (2x^2+6x+a)\] the first formula has an x<-6 and the 2nd has x</=-6 and i have to find which value would make it continuous. i set them equal to each and plugged in -6 in for the x and solved for a getting -36 which is wrong