MaxWong

\(\frac{1}{2}(6x+4)=x+2(x+1)\\ 3x+2=x+2x+2\\ 3x+2 = 3x + 2\\ \therefore\text{This equation have infinite solutions and cannot be solved.}\)

Btw LOL it's not the hardest maths in the world it's only inequalities......

We have to use implicit differentiation.

\(y=x^x\\ \ln y = x \ln x\\ \dfrac{\mathtt dy}{\mathtt dx}\dfrac{1}{y}=\ln x+1\text{ <-- product rule}\\ \dfrac{\mathtt dy}{\mathtt dx}=y(\ln x + 1)\\ \;\;\;\;\;\;\!=x^x\ln x + x^x\)

Bye Santos :D

LOL 

For the a≈ pi *a` /180º part.

That is an identity. That's the degree and radians conversion formula and it applies for any values.

a \(\equiv\) pi *a` /180º

0.9tan a = sin a

sin a / tan a = 0.9

cos a = 0.9

a = arccos 0.9 ≈ 0.451026811796 rad.

For sin a ≈ a part.....

Use my triangle above.

As theta approaches 0, b approaches 0, b/c approaches 0, therefore sin theta approaches 0

This can be represented as \(\displaystyle\lim_{\theta\rightarrow0}\sin \theta=0\)

Therefore for small values, sin a ≈ a

Show that for small angles under 20º that tan a ≈ sin a?

Construct a right-angled triangle with angle theta and 3 side lengths = a,b, and c. 

Just like this:

As theta decreases, sin theta=b/c decreases, therefore b decreases, therefore cos theta approaches 1, therefore a ≈ c, therefore b/a ≈ b/c, therefore tan theta ≈ sin theta.

x>1 and y< -1 means x>y.

Yea C is correct. 

Different variables with same operations. if x>y, f(x)>f(y)