lim as x approaches 0 of (1-cos4x)/(9x^2)

I know its 8/9 but I don't know how to get there
in Trigonometry Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

cosθ=1-θ2/2!+θ4/4!-θ6/6!

If θ=4x, this becomes: cos(4x)=1-16x2/2+256x4/24-etc.

1-cos(4x)=16x2/2-256x4/24+etc.=8x2-64x4/6, so:

(1-cos(4x))/(9x2)=8x2/9x2=8/9 as x→0.

by Top Rated User (1.2m points)

Related questions

1 answer
lim as (x) approaches 0 of (sin^2(x))/2x
asked Sep 17, 2015 in Trigonometry Answers by anonymous | 756 views
1 answer
find the lim of sinx-sin1/x-1 as x approaches 1
asked Feb 6, 2013 in Trigonometry Answers by anonymous | 1.9k views
1 answer
lim as x,y approaches 0,0 of xysin(1/xy))
asked Mar 30, 2013 in Calculus Answers by anonymous | 1.2k views
1 answer
lim as x approaches 0 of x(sin(1/x))
asked Mar 11, 2013 in Calculus Answers by anonymous | 1.1k views
1 answer
lim as x approaches pi of 6sin(x+sinx)
asked Feb 25, 2013 in Calculus Answers by anonymous | 632 views
1 answer
find the lim using of sinx-sin1/x-1 as x approaches 1
asked Feb 6, 2013 in Calculus Answers by anonymous | 773 views
1 answer
lim as x approaches pi of (1+sinx)/2x
asked Jan 13, 2013 in Calculus Answers by anonymous | 1.0k views
1 answer
lim x approaches 0 6x-9/x^3-12x+3
asked Nov 16, 2013 in Calculus Answers by honey | 1.3k views
1 answer
lim x approaches 0 in cos(45-x)/x
asked May 29, 2013 in Calculus Answers by anonymous | 975 views
1 answer
lim x approaches pi of (x-pi) / sinx
asked Mar 11, 2012 in Calculus Answers by anonymous | 2.3k views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!

Most popular questions within the last 3000 days

  1. 50+50-25X0+2+2= (19)
  2. it takes 10 road workers 5 days to complete a road repair when working 2 hours a day.Working at the same pace,how many days will it take 2 people working 5 hours a day to finish it? (3)
  3. Solve 15 -1(12÷4+1)? (4)
  4. 8:4(5+2) (3)
  5. How can i represent 1/3; 3/3; 7/3; 10/3 and 15/3 on a number line? (1)

Most popular tags

87,516 questions
100,279 answers
2,420 comments
731,876 users