# Completing The Square (Why It Works)

Prove that:

Proof:

Second Proof:

Prove that:

Proof:

Second Proof:

# Obtaining The Mean From Two Sets Of Data

Prove that if set A, of size , has mean and set B, of size , has a mean then the **mean of the combined** set of A and B is .

——————

Set A:

Therefore:

Therefore:

——————

Set B:

Therefore:

Therefore:

So:

# How To Deal With Fractions

# Tough Logarithmic Problem…

# If y=e^(f(x)), dy/dx=f'(x)e^(f(x))

Proof:

# If y=e^x, dy/dx=e^x

Prove that:

Say that:

And that:

Therefore:

# If y=a^x, dy/dx=a^xlna proof

# If y=lnx, dy/dx=1/x proof

Now: