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Numerical evidence of Calculus Limits?
Obviously you can't show me the graph but the numerical part would help. (i already know what the graph looks like).Use numerical and graphical evidence to guess the value of the limit . Also how close to 1 does x have to be to ensure that the function is within a distance of 0.5 of its limit?
Lim
X---->1
(x^3-1) / (√x - 1)
1 Answer
- Seamus OLv 71 decade agoFavorite Answer
lim as x →1 (x^3 - 1) / (√x - 1)
= lim as x →1 [(x - 1)(x^2 + x + 1)(√x + 1)] / [(√x - 1)(√x + 1)]
[Factoring (x^3 - 1) to (x - 1)(x^2 + x + 1) using the difference of cubes identity and then rationalizing the denominator by multiplying both the numerator and the denominator by the conjugate surd √x + 1]
= lim as x →1 [(x - 1)(x^2 + x + 1)(√x + 1)] / (x - 1)
= lim as x →1 (x^2 + x + 1)(√x + 1) [Because the (x - 1)'s cancel]
= (1 + 1 + 1)(1 + 1) [Taking the limits]
= 3 x 2
= 6
