Hey, having some trouble.
The limit as X approaches infinity of (sqrt(3x^2+8x+6)-sqrt(3x^2+3x+1))
Thinking about the problem, it seems that X would approach 0 in an infinity minus infinity case. However, my teacher has taught that an infinity minus infinity case is never equal to zero, even in comparable forms of infinity (for example, x^2 minus X^2 as X approaches infinity would not equal 0). Rather, he says that the problem needs to be rephrased.
I have tried multiplying (1/X)/(1/X) through (using 1 as the denominator for both terms originally in the limit), and while that works to get a limit for the top of the fraction, the 1/X in the denominator approaches zero and seems to have no way to be dealt with.
Any help is appreciated--thanks!
The limit as X approaches infinity of (sqrt(3x^2+8x+6)-sqrt(3x^2+3x+1))
Thinking about the problem, it seems that X would approach 0 in an infinity minus infinity case. However, my teacher has taught that an infinity minus infinity case is never equal to zero, even in comparable forms of infinity (for example, x^2 minus X^2 as X approaches infinity would not equal 0). Rather, he says that the problem needs to be rephrased.
I have tried multiplying (1/X)/(1/X) through (using 1 as the denominator for both terms originally in the limit), and while that works to get a limit for the top of the fraction, the 1/X in the denominator approaches zero and seems to have no way to be dealt with.
Any help is appreciated--thanks!
