As a maths-related blog, many of you here have been deprived of a question containing that most iconic of mathematical symbols: the sexy and alluring integral symbol with her … errm … 10-2-10 curvaceous figure.

Hence, Miss Loi shall not deprive you further …

Differentiate ln(cos 2x) with respect to x. Hence, or otherwise, evaluate

Please, please note the word Hence in the question! The words “or otherwise” are usually placed there just for show, unless you like to do things the long way. Hence Miss Loi terms these Hence Questions.

If that’s not clear enough, the Hence is meant to remind you to use information from your answer/workings in an earlier part to solve the next part. Sounds easy but sometimes it’s not so straightforward and you’ll usually need to think of one more step before attaining enlightenment.

Differentiation and Integration are a match made in heaven. So unless they are having a tiff, there’s a good chance you’ll see them together in the same question. Miss Loi has observed that many students got so enchanted by the sexy integral sign that they totally forgot about their differentiation techniques, and vice versa for those with more … errmmm … ‘differential’ tastes.

So whenever you spot the word Hence, remember to 看前面 (watch your front again)!!!

This is the key part of this hence question: expressing tan 2x as a differential using your earlier answer. May Heaven help you if you're trying to integrate tan 2x on your own! (At least if you're an O-Level student anyway :P)

.'.

=

=

= (corr. to 5 sig. fig.) CORRECTO!

A little thought on the integral sign: it looks more like the figure just under the strings of a violin, but I do agree that it is rather like a tangent curve. My E+A-math teacher says tangent curves are like "pretty ladies in a beauty pageant".

OMG the pageant must be held outdoors since tangent curves tend to reach high into infinity! Sorry lame math jokes I know ...

And when I put E and A together I instantly thought of the slogan of EA games (I don't play any EA games, though): EA Games - Challenge Everything.

Waiting for more math challenges! Stay tuned 😉

p.s. the math expressions are all stuck together because when I tried to separate them there was always some problems with the display.

* Please refer to the relevant Ten-Year Series for the questions of these suggested solutions.

About Miss Loi

Miss Loi is a full-time private tutor in Singapore specializing in O-Level Maths tuition. Her life’s calling is to eradicate the terrifying LMBFH Syndrome off the face of this planet. For over years she has been a savior to countless students … [read more]

Gratitudes

It is not an overstatement when I say that she has so far been the best tuition teacher I have ever had!! … [read more]

## 2 Comments

曜

日

Yup remember your here!

.'.

This is the key part of this

hencequestion: expressing tan 2xas a differential using your earlier answer. May Heaven help you if you're trying to integrate tan 2xon your own! (At least if you're an O-Level student anyway :P).'.

=

=

= (corr. to 5 sig. fig.) CORRECTO!

A little thought on the integral sign: it looks more like the figure just under the strings of a violin, but I do agree that it is rather like a tangent curve. My E+A-math teacher says tangent curves are like "pretty ladies in a beauty pageant".

OMG the pageant must be held outdoors since tangent curves tend to reach high into infinity! Sorry lame math jokes I know ...

And when I put E and A together I instantly thought of the slogan of EA games (I don't play any EA games, though):

EA Games - Challenge Everything.Waiting for more math challenges! Stay tuned 😉

p.s. the math expressions are all stuck together because when I tried to separate them there was always some problems with the display.

曜

日

well explined and worth