Use l’Hôpital’s rule to find lim(csc(x) - cot(x)) as x -> 0.

This question relies partially on remembering the trigonometric identities, csc(x) = 1/(sin(x)) and cot(x) = 1/(tan(x)) = cos(x)/sin(x). Plugging these values into the equation, we want to find Lim((1-cos(x))/sin(x)) as x -> 0.

l'Hôpital's rule states that we can differentiate the top and bottom of the fraction separately and the limit will stay the same (note: we are not differentiating the fraction as a whole, this requires the quotient rule, but instead differentiating the numerator and denominator individually).

We do so to get that the limit is now Lim((sin(x)/cos(x)) as x -> 0 which is just 0. Therefore, the limit of the original equation is 0.

Felix S. IB Maths tutor, 11 Plus Maths tutor, GCSE Maths tutor, 13 pl...

5 months ago

Answered by Felix, an IB Further Mathematics tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£24 /hr

Aran D.

Degree: BSc Mathematics (Bachelors) - York University

Subjects offered: Further Mathematics , Maths+ 1 more

Further Mathematics

“I am a friendly and professional software engineer and maths graduate with first class honours. I have experience tutoring GCSE, A-level and undergraduate level maths, as well as key stage 3 Spanish. I also have four years' experience ...”

MyTutor guarantee

£20 /hr

Jay L.

Degree: Mathematics, Operational Research, Statistics and Economics (MORSE) (Bachelors) - Warwick University

Subjects offered: Further Mathematics , Maths+ 4 more

Further Mathematics
-Personal Statements-

“Hi! I am currently a fresher at the University of Warwick, studying Maths, Operational Research, Statistics and Economics, or MORSE. I have always enjoyed the challenge of maths and would really like to help you experience joy and sa...”

£20 /hr

Szymon K.

Degree: Mechanical Engineering (Masters) - Manchester University

Subjects offered: Further Mathematics , Physics

Further Mathematics

“About me: I am a student pursuing my degree in Mechanical Engineering at the University of Manchester. Ever since I can remember I have always been passionate about passing my knowledge to others. As a tutor I taught people of differen...”

About the author

Felix S.

Currently unavailable: for new students

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Further Mathematics , Maths

Further Mathematics

“About me: Hi, I'm Felix and I'm currently studying for a Mathematics degree at Warwick University. I am very keen to show people not just how to pass maths exams, but how to actuallyenjoy the subject too! I got A* in GCSE Maths and th...”

You may also like...

Posts by Felix

Express 0.545454... as a fraction in its simplest form.

Given a^2 < 4 and a+2b = 8. Work out the range of possible values of b. Give your answer as an inequality.

Prove that the function f:ZxZ -> ZxZ defined by f(x,y) = (2x+y,x+y) is a bijetion.

Sunita has 75 pens and she ties them into bundles of 8. How many pens does she have left over?

Other IB Further Mathematics questions

Prove that i^i is real.

Prove that the function f:ZxZ -> ZxZ defined by f(x,y) = (2x+y,x+y) is a bijetion.

Use l’Hôpital’s rule to find lim(csc(x) - cot(x)) as x -> 0.

View IB Further Mathematics tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss