592 views

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.

1 year ago

Answered by Felix, an IB Further Mathematics tutor with MyTutor

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

13 SUBJECT SPECIALISTS

£26 /hr

Degree: MMath Mathematics with Placement (Masters) - Bath University

Subjects offered:Further Mathematics , Maths+ 4 more

Further Mathematics
Maths
Italian
Computing
.STEP.
.MAT.

£20 /hr

Degree: Mathematics (Bachelors) - Bath University

Subjects offered:Further Mathematics , Maths

Further Mathematics
Maths

“Hi, I’m Sachin and I study Maths at the University of Bath. I’m looking forward to working with my students to enable them to reach their highest potential.”

£20 /hr

Degree: Mechanical Engineering (Masters) - Manchester University

Subjects offered:Further Mathematics , Physics+ 2 more

Further Mathematics
Physics
Maths
.PAT.

“"It is the supreme art of the teacher to awaken joy in creative expression and knowledge." Albert Einstein”

Currently unavailable: for new students

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Further Mathematics , Maths

Further Mathematics
Maths

“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...”

MyTutor guarantee

|  1 completed tutorial

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

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

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

Prove that i^i is real.

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.