calculus limits at infinity. best answer gets points?

Question

Math limits at infinity?

Evaluate the limit.



2. lim \/x^3-2x^2+1]/[x-1]
x-->+infinity
4. lim [\/1+\/x]/ [\/1+x]
x-->+infinity
6. lim [^3\/x^3+2] - [^3\/x^3-1]
x-->-infinity
7. lim[ x^2-1]/ [\/x^2+1]
x-->-infinity
8. lim [\/x^2-2x+3 - \/x]
x-->+infinity
10. lim [\/x^3-4x^2+1] + [\/x^2-x] +x

Answer 1

2. lim \/x^3-2x^2+1]/[x-1] = lim x \/x - 2/x2 + 1/x^2]/[{x +1] =
lim x/(x +1) * lim \/x - 2/x2 + 1/x^2
As x --> oo, x/( x +1) --> 1 and x - 2/x2 + 1/x^2 --> oo, which implies \/x - 2/x2 + 1/x^2 --> oo. Therefore,
lim \/x^3-2x^2+1]/[x-1] = oo
x-->+infinity

The other exercises are similar

Answer 2

specially, something that oscillates diverges. by using fact this might nicely be a series, and you at the instant are not including any words, it particularly is going to converge to 0 by using fact the denominator is increasing to countless. It being unfavourable or beneficial wont make a difference by using fact it is so close to to 0.

Answer 3

2.divid by x
=0

Answer 4

take derivative of numerator and denominator of each fraction

Answer 5

the limit is infinity....


where on earth can you apply calculus???!!!