- #1

- 114

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## Homework Statement

hello, what can I do to solve this without using d'hospital method?

[tex]\lim_{x\to0}\frac{\tan x-x}{x^3}[/tex]

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- Thread starter player1_1_1
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- #1

- 114

- 0

hello, what can I do to solve this without using d'hospital method?

[tex]\lim_{x\to0}\frac{\tan x-x}{x^3}[/tex]

- #2

- 24

- 0

## Homework Statement

hello, what can I do to solve this without using d'hospital method?

[tex]\lim_{x\to0}\frac{\tan x-x}{x^3}[/tex]

Recall the formula [which is just the M.S. for tan(x)]:

[tex]tan(x)=x+\frac{1}{3}x^3+\frac{2}{15}x^5+\frac{17}{315}x^7+...[/tex]

Substitute this in the limit and the two "x" will be cancelled.

Then divide the denominator and the numerator by x^3.

and the limit will be done by the direct substitution.

The limit = 1/3

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