Logarithmic and exponential functions assignment help (1 Viewer)

[Miz Janani]

12. Logarithmic and Exponential Functions​

12.1 Review of index laws, and definition of ar for a > 0, where r is rational.

^^^
that's from the syllabus...

Can anyone explain to me what the latter part of the syllabus point is?

So...

What is the definition for ar for a > 0, where r is rational?

Thanx in advance for any help...

 

[shuning]

回复: Logarithmic and exponential functions assignment help

.... that's not how u study math T.T
for other subjects u can read the syllbus... but not math LOL

 

[Miz Janani]

It's for an assignment.. and it's the only way i'll get 100%.. so im like super confused..

and shouldn't you be studying?? Hmmm..

 

[shuning]

回复: Re: Logarithmic and exponential functions assignment help

WOW GG to ur school xD
having done the 2u HSC last yr...... ive never came across something like this b4... WTF assignment in math LOL and u actually have to do internet research for math.... WOW what a gg teacher...

 

[Miz Janani]

And ironically you just skipped over my question.. But at least you're helping others..

 

[Trebla]

Read p66 of the syllabus at the very bottom:
"If a > 0 and r = p/q, then a^r is defined as the q-th root of a^p"

If r is rational it can be expressed as a fraction p/q where p and q are integers with no common factors (other than 1).

 

[Miz Janani]

In understandable language please...

 

[addikaye03]

In understandable language please...

The concept is stated perfectly by Trebla, in english for that matter. A value/pronumeral is called 'rational' if it can be expressed as a fraction p/q where p and q are integars, and may only share the factor of 1 ie. factors of 5 are 1,5... factors of 7 are 1,7 etc etc

I tried to state it differently but its no use, its stated precisely above

 

[Miz Janani]

Oh..

It just clicked..

Thankyou

 

[addikaye03]

Oh..

It just clicked..

Thankyou

yer sorry i couldn't help anymore.

 

[Miz Janani]

No that's fine.

One more question..

How would you answer this question:

Q: Find the area under the curve y=e^2x between x=1 and x=1.

I know that the derivative of e^2x is e^2x, but how do i find the primitive??

So confused

 

[addikaye03]

No that's fine.

One more question..

How would you answer this question:

Q: Find the area under the curve y=e^2x between x=1 and x=1.

I know that the derivative of e^2x is e^2x, but how do i find the primitive??

So confused

Although d/dx(e^1x)=1e^x, this is only because the coefficient (number in front) of x is a 1, so ignore the 1. BUT d/dx(e^2x)=2e^2x, same as d/dx(e^3x)=3e^3x... so just be careful there.

The general rule for integration with exponentials also involves the coefficient. int.(e^x)=e^x
but int(e^2x)=1/2(e^2x)+C... so the gereral rule:

int. (e^ax)=(1/a)(e^ax)+C... do you see what i mean?

Try and answer your Q now, if you still have trouble then let me know and i will talk you through it.

 

[Miz Janani]

I kind of made a mistake when writing that question..

Its between x=1 and x=3

Sorry about that...

 

[samthebear]

Primitive of e^2x would be (1/2)(e^2x) simply because the derivative (which is e^2x) has no number out the front of e. Where there is no number out the front, there is a 1, but because it's just 1 it is not written in (1 multiplied by anything is the same thing ie: 1x = x same goes for e. 1e = e).

If you simply differenciated e^2x, you'll get 2e^2x. but because the differenciated term only has e^2x with a 1 out the front, you need something multiplied by the 2 (in 2e^2x which is the stright forward differenciated term) to make it 1. and that would be 1/2. so:

Intergral of e^2x (< this is the differenciated term)
= (1/2)(e^2x) (< this is the primitive or intergrated term)

 

[tommykins]

primitive*