The least positive integer n for which - n -1- n -1-12 isA- 6B- 7C- 8D- 9

The correct option is C 8 (n + 1)^1/3 (n)^1/3 lt; 1/12 (n + 1)^1/3 lt; (n)^1/3 + 1/12 Cube both side are get (n^1/3)( n^1/3 + 1/12) gt; 1727/432 So, n ...

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Standard XII

Mathematics

Composite Function

The least pos...

Question

The least positive integer n for which $\sqrt[3]{n + 1} - \sqrt[3]{n} < \frac{1}{12}$ is

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Solution

The correct option is C
8

$(n + 1)^{1 / 3} - (n)^{1 / 3} < \frac{1}{12}$

$(n + 1)^{1 / 3} < (n)^{1 / 3} + \frac{1}{12}$

Cube both side are get

$(n^{1 / 3}) (n^{1 / 3} + \frac{1}{12}) > \frac{1727}{432}$

So, n = 8 only possible least positive integer.

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The least positive integer n for which 3√n+1−3√n<112 is

The correct option is C 8 (n+1)1/3−(n)1/3<112 (n+1)1/3<(n)1/3+112 Cube both side are get (n1/3)(n1/3+112)>1727432 So, n = 8 only possible least positive integer.

The least positive integer n for which $\sqrt[3]{n + 1} - \sqrt[3]{n} < \frac{1}{12}$ is

The correct option is C
8

$(n + 1)^{1 / 3} - (n)^{1 / 3} < \frac{1}{12}$

$(n + 1)^{1 / 3} < (n)^{1 / 3} + \frac{1}{12}$

Cube both side are get

$(n^{1 / 3}) (n^{1 / 3} + \frac{1}{12}) > \frac{1727}{432}$

So, n = 8 only possible least positive integer.