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.

Question

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.

jim_thompson5910 · Answer

`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 $\Large \infty - \infty$

jim_thompson5910 · Answer

sorry it's spelled "indeterminate"

anonymous · Answer

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?

jim_thompson5910 · Answer

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