- #1
snoopies622
- 846
- 28
A quiz at the end of Steven Krantz's Calculus Demystified includes the following problem:
Find
[tex]
\lim_{x \to \infty} [ \sqrt[3]{x+1}
-
\sqrt[3]{x} ]
[/tex]
I see how one can use the Maclaurin series to get
[tex]
\sqrt[3]{x+1} = 1 + \frac {x}{3} - \frac {x^2}{9} + \frac {5 x^3}{81} + . . .
[/tex]
but trying it with the cube root of x gives me zero plus an endless series of undefined terms.
Is there a way to expand [itex] \sqrt[3]{x} [/itex] and solve this problem?
Find
[tex]
\lim_{x \to \infty} [ \sqrt[3]{x+1}
-
\sqrt[3]{x} ]
[/tex]
I see how one can use the Maclaurin series to get
[tex]
\sqrt[3]{x+1} = 1 + \frac {x}{3} - \frac {x^2}{9} + \frac {5 x^3}{81} + . . .
[/tex]
but trying it with the cube root of x gives me zero plus an endless series of undefined terms.
Is there a way to expand [itex] \sqrt[3]{x} [/itex] and solve this problem?