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Limes without d'hospital

  • #1
114
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]
 

Answers and Replies

  • #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 devide the denominator and the numerator by x^3.
and the limit will be done by the direct substitution.
The limit = 1/3
 
  • #3
67
0
look up the taylor series for sin and cosine and write the one for tan. Now factor out X^3 from the top and take that limit as X goes to Zero
 

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