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Solve this problem lim->0 (sinx - x + x 3 ) /x 5 this is 0/0 lim expansion

Solve this problem                                            lim->0 (sinx - x + x3) /x5                                                                                                                                                                                                                        this is 0/0 lim expansion 

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Grade:12

1 Answers

Arun
25750 Points
4 years ago
Dear student
Use expansion of sinx = x – x^3/3! + x^5/5! – x^7/7! + …....
 
hence in Question we are left with
 
(x^5/5! – x^7/7! + …....)/x^5
 
now take x^5 common from numeratpr and put the limit x = 0
 
answer of limit is 1/5! = 1/120

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