## anonymous one year ago I would like to know if I am understanding the concept of limits and derivatives limx→1 (x^2+3x−4) / (x^2+8x−9) =(limx→1(x^2+3x−4)) / (limx→1 (x^2+8x−9)) This is false because the first part equals 1/2 and the second part is indeterminate If f′(2) exists, then then the limit limx→2f(x) is f(2) This is true because there is continuity. If limx→3f(x)=∞ and limx→3g(x)=∞, then limx→3[f(x)−g(x)]=0 This is true because of the limit law of quotient. If limx→2[f(x)g(x)] exists, then the limit is f(2)g(2) This is true because of the limit law of product.

1. jim_thompson5910

If limx→3f(x)=∞ and limx→3g(x)=∞, then limx→3[f(x)−g(x)]=0  This is true because of the limit law of quotient. I don't agree. Recall that one of the many indeterminant forms is $$\Large \infty - \infty$$

2. jim_thompson5910

sorry it's spelled "indeterminate"

3. anonymous

Oops, I meant the limit law of difference not quotient. However, I now recalled that indeterminate form. So that statement would be entirely false because it is indeterminate?

4. jim_thompson5910

yeah limx→3[f(x)−g(x)] is indeterminate and not equal to 0