MaxWong

Yea I agree :)

The calculator does some calculus too :):)

It is more clever than me :)

~The smartest cookie in the world.

$\ln(|8|) - \ln(|1|)\\ =\ln\left(\dfrac{|8|}{|1|}\right)\\ = \ln 8$

Or is it? :)

$\dfrac{10^6}{20}\\ =\dfrac{2^6\times 5^6}{2^2 \times 5}\\ \text{Therefore not co-prime......}$

3x + 4(x - 2) + 1

= 3x + 4x - 8 + 1

= 7x - 7

I think of $e^{i\theta} = \cos \theta + i\sin \theta$......

Let me try :) (Im just a kid don't blame me if I did anything wrong....... Just point out the mistake......)

$4\sin x = e^{x}\\ 4\sin x = e^{(i^4 \cdot x)}\quad\boxed{i^4 = 1}\\ 4\sin x = e^{i\cdot(xi^3)}\\ 4\sin x = e^{i\cdot(-ix)}\quad\boxed{i^3 = -i}\\ 4\sin x = \cos(-ix)+i\sin(-ix)$

We are going to introduce 4 formulae here:

1) $\sin(-x) = -\sin x$

2)$\cos(-x) = \cos x$

3)$\cos(ix) = \cosh x = \dfrac{e^x + e^{-x}}{2}$

4)$\sin(ix) = i\sinh x = \dfrac{e^{-x} - e^{x}}{2i}$

Now continue.....

Last step done was:

 $4\sin x = \cos(-ix) + i\sin(-ix)\\ 4\sin x = \cos(ix) -i\sin(ix)\quad\boxed{\text{Formulae 1 and 2}}\\ 4\sin x = \dfrac{e^x + e^{-x}}{2}+\dfrac{e^x - e^{-x}}{2}=e^x\quad\boxed{\text{Formulae 3 and 4}}$

Nope it just goes back to 4 sin x = e^x....... Sob sob :(

Another method!!

$4\sin x = e^x\\ $

We are going to introduce the definition of sin x this time....... (If it doesn't work Im going to use Taylor series :( )

$4\left(\dfrac{e^{ix}-e^{-ix}}{2i}\right) = e^x\\ \dfrac{2e^{ix}-2e^{-ix}}{i}=e^x\\ 2ie^{-ix} - 2ie^{ix} = e^x\quad\boxed{\dfrac{1}{i} = -i}\\ 2i\left(\dfrac{1}{e^{ix}}-e^{ix}\right)=e^x\\ 2i\left(\dfrac{1-e^{2ix}}{e^{ix}}\right)=e^x$

Np.

I never give up!!!

Another method!!

$4\left(x-\dfrac{x^3}{3!}-\dfrac{x^5}{5!}+\dfrac{x^7}{7!}+\dfrac{x^9}{9!}\cdot \cdot\; \cdot\right)=e^x$

Still np......

Sigh maybe I am just too dull and can't see the method...... 

PS I am 14 :)

The product contains an element which evaluates to 0. Therefore A = 0.

The banana is right in the stomach of the fish so you can't see it. Look carefully! LOL

~The smartest cookie in the world.

Yea. There are always some people answering :)

450 x 525

= 236250

40x - 8

= 8(5x - 1)

:)

~The smartest cookie in the world.