anonymous
  • anonymous
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.
Mathematics
jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • 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 \(\Large \infty - \infty\)
jim_thompson5910
  • jim_thompson5910
sorry it's spelled "indeterminate"
anonymous
  • 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?

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jim_thompson5910
  • jim_thompson5910
yeah `limx→3[f(x)−g(x)]` is indeterminate and not equal to 0

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