Hmmmm judging by the values in between integers, like 2.5, 1.5, -2.5, -3.5 and so on, those values always produce a smaller number hmm that sounds whack... lemme put it differently.

a floor() function, namely ⌊x⌋ like that, will floor the decimal values, so ⌊2.5⌋ floors to 2, because 2.5 is between 2 and 3, and the smallest is 2, the "floor", the 3 will be the "ceiling".

so for a floor function, ⌊1.5⌋ is 1, 1.5 is between 1 and 2, 1 is the smallest, ⌊-3.5⌋ is -4, recall that on the negative side, the closer to 0, the larger, so -1 is much larger than -1000.

and say ⌊-1.35⌋ is -2, -1.35 is between -2 an -1 and -2 is the smallest, the "floor".

that said

x = 2.5 ⌊ 2.5 + 3⌋ is ⌊5.5⌋ which is 5

x = 1.5 ⌊ 1.5 + 3 ⌋ is ⌊4.5⌋ which is 4

x = -2.749 ⌊ -2.749 + 3⌋ is ⌊0.251⌋ which is 0

anyway and so on, so you can pretty much see is the floor function of ⌊ x + 3⌋.

6 0

3 years ago

How to solve this limit?

wlad13 [49]

(2x^2/(1-x^2)) + 3^(1/x) for the first half you can simply divide all terms by the highest power of x to get:

2/(1/x^2-1) as x approaches infinity you have 2/-1=-2

For the second part the exponent approaches zero as x approaches infinity and anything raised to the zero power is equal to 1 so you have:

-2+1=-1

So the limit as x approaches infinity is -1.

3 0

4 years ago

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