GATE CSE
First time here? Checkout the FAQ!
x
+2 votes
128 views

asked in Calculus by Veteran (14.6k points)   | 128 views

1 Answer

+4 votes
Best answer

cos(x) = 1 - x2/2! + x4/4! - x6/6! + ... 
sin(x) = x/1! - x3/3! + x5/5! - x7/7! + ... 
cosh(x) = 1 + x2/2! + x4/4! + x6/6! + ... 
sinh(x) = x/1! + x3/3! + x5/5! + x7/7! + ... 
   sinh(x)-sin(x)=2x3/3!+......
cosh(x)-cos(x)=2x2/2! +.....
limx->0 ( sinh(x)-sin(x) /x(cosh(x)-cos(x))
limx->0  (2x3/3!)/x*(2*x2/2! )=2/3!= 1/3

answered by Veteran (10.5k points)  
selected by
Why did you neglect the higher order terms in the maclaurin series expansion in the last step? Is it some kind of approximation we need do?
bcoz all of those becomes 0 during calc on x->0
Do you always follow this way with trignometric functions.
any other way to solve this instead of the series expansion?


Top Users Apr 2017
  1. akash.dinkar12

    3366 Points

  2. Divya Bharti

    2536 Points

  3. Deepthi_ts

    2040 Points

  4. rude

    1966 Points

  5. Tesla!

    1768 Points

  6. Shubham Sharma 2

    1610 Points

  7. Debashish Deka

    1584 Points

  8. Prashant.

    1462 Points

  9. Arunav Khare

    1444 Points

  10. Kapil

    1414 Points

Monthly Topper: Rs. 500 gift card

22,072 questions
28,030 answers
63,194 comments
24,128 users