Unorthodox Core 2 question ?

username193837

http://www.mei.org.uk/files/papers/c208ja_kf9x.pdf

For question 12 ii C and D (the two final questions).

What does find lim *arrow* 0 mean and what does state what this limit represents mean.

I have honestly never seen this type of question ever inn core 2, the mark scheme is underneath.

Reply 1

L'Evil Fish

18

Haven't opened, but lim --> 0

Means you let a variable (probably x) tend to 0

Reply 2

emily288

2

You have to use differentiation from first principles

Reply 3

username193837

OP

17

Original post by L'Evil Fish

Haven't opened, but lim --> 0

Means you let a variable (probably x) tend to 0

How do you let it tend to 0

Reply 4

username193837

OP

17

Original post by emily288

You have to use differentiation from first principles

How do you use that ?

Reply 5

L'Evil Fish

18

Original post by 96jaimin96

How do you let it tend to 0

basically let it =0

Reply 6

Zen-Ali

8

Original post by 96jaimin96

How do you use that ?

If you use a limit, you let something 'tend' to a value, because substituting in the actual value may give you something that is undefined.

E.g., if I asked you to evaluate

\displaystyle\lim_{x \to 0} \dfrac{1}{x}

You would start with any number for

x

, and then keep on substituting in smaller and smaller values of

x

. (This is because we're letting

x

tend to 0; if, for example, we let

x

tend to infinity, we would substitute in larger and larger values of

x

).

E.g.,

\displaystyle\lim_{x \to 0} \dfrac{1}{x}

where

x = 1

gives you

1

.

Then, using a smaller value of

x

, we have

\displaystyle\lim_{x \to 0} \dfrac{1}{x}

where

x = \dfrac{1}{2}

gives you

2

.

To illustrate this now by using a very small value of

x

, we have

\displaystyle\lim_{x \to 0} \dfrac{1}{x}

where

x = \dfrac{1}{50}

gives you

50

, which implies that

\displaystyle\lim_{x \to 0} \dfrac{1}{x} = \infty.

This is the general idea of limits. Within the context of the question, they want you to use the limit definition of a derivative, which pertains to letting a small increase in

x

tend to 0, giving you the gradient (this is differentiation from first principles); you should read about this further on Wikipedia/YouTube.

Edit: why does the LaTeX version of 0 not display? :lol:

(edited 9 years ago)

Reply 7

username193837

OP

17

Original post by Zen-Ali

If you use a limit, you let something 'tend' to a value, because substituting in the actual value may give you something that is undefined.

E.g., if I asked you to evaluate

\displaystyle\lim_{x \to 0} \dfrac{1}{x}

You would start with any number for

x

, and then keep on substituting in smaller and smaller values of

x

. (This is because we're letting

x

tend to 0; if, for example, we let

x

tend to infinity, we would substitute in larger and larger values of

x

).

E.g.,

\displaystyle\lim_{x \to 0} \dfrac{1}{x}

where

x = 1

gives you

1

.

Then, using a smaller value of

x

, we have

\displaystyle\lim_{x \to 0} \dfrac{1}{x}

where

x = \dfrac{1}{2}

gives you

2

.

To illustrate this now by using a very small value of

x

, we have

\displaystyle\lim_{x \to 0} \dfrac{1}{x}

where

x = \dfrac{1}{50}

gives you

50

, which implies that

\displaystyle\lim_{x \to 0} \dfrac{1}{x} = \infty.

This is the general idea of limits. Within the context of the question, they want you to use the limit definition of a derivative, which pertains to letting a small increase in

x

tend to 0, giving you the gradient (this is differentiation from first principles); you should read about this further on Wikipedia/YouTube.

Just watched a video from youtube, so basically you just substitute h for 0 and you get left with 4x^3. Thanks you taking the time to give a long explanation.

Reply 8

Zen-Ali

8

Original post by 96jaimin96

Just watched a video from youtube, so basically you just substitute h for 0 and you get left with 4x^3. Thanks you taking the time to give a long explanation.

[Indent]I hope I didn't make any mistakes. :ninja:

No worries, man.[/Indent]

Reply 9

davros

16

Original post by 96jaimin96

http://www.mei.org.uk/files/papers/c208ja_kf9x.pdf

For question 12 ii C and D (the two final questions).

What does find lim *arrow* 0 mean and what does state what this limit represents mean.

I have honestly never seen this type of question ever inn core 2, the mark scheme is underneath.

Are you actually being taught the MEI syllabus by your teacher?

The method displayed in this question is basically showing you an example of "differentiation from first principles" which is something that all teachers should explain but unfortunately not all do, although not all the exam boards seem to test this!

Reply 10

ThatPerson

18

Original post by Zen-Ali

[Indent]I hope I didn't make any mistakes. :ninja:

No worries, man.[/Indent]

Spoiler

Reply 11

Zen-Ali

8

Original post by ThatPerson

Spoiler

Thanks for reminding! I decided to omit that and some other stuff in case it got confusing.

@OP, if you're interested about what the person above me posted, you should check: https://www.khanacademy.org/math/differential-calculus/limits_topic/old-limits-tutorial/v/limit-examples--part-2.

(edited 9 years ago)

Reply 12

username193837

OP

17

Original post by davros

Are you actually being taught the MEI syllabus by your teacher?

The method displayed in this question is basically showing you an example of "differentiation from first principles" which is something that all teachers should explain but unfortunately not all do, although not all the exam boards seem to test this!

Never got taught this, but I am kind of self teaching, and their are not many online (video) resources for MEI like their is for Edexcel.

Unorthodox Core 2 question ?

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