what is the limit of the function (1-sin x)/cos^2 x, x -> 90 degrees?
Expert Answers
Tushar Chandra
| Certified Educator
| Certified Educator
calendarEducator since 2010
write12,551 answers
starTop subjects are Math, Science, and Business
We have to find the value of lim x--> 90[ (1- sin x)/(cos x)^2]
substituting x = 90 degrees, we get the indeterminate form 0/0, so we can use l'Hopital's rule and substitute the numerator and denominator by their derivatives.
=> lim x->90 [ (- cos x)/ (-2 cos x * sin x)]
=> lim x->90 [ 1/ (2 sin x)]
substitute x = 90
=> 1/ 2
The required value of lim x--> 90[ (1- sin x)/(cos x)^2] is (1/2).
Related Questions
- How to evaluate the limit of (cos x - cos 3x) / x*sin x if x-->0 ?
- 1 Educator Answer
- Verify if limit of ln(1+x)/x is 1, x-->0
- 1 Educator Answer
- Prove that limit of the function (a^x-1)/x=lna,x->0,using two methods.
- 1 Educator Answer
- What is the limit of the function sin x/(1-2sin^2x) -cos x/(2cos^2x-1) - sin2x/cosx, if x...
- 1 Educator Answer
- Determine the limit of the function (sin5x-sin3x)/x, x-->0
- 1 Educator Answer