Algebraic substitutions
Trigonometric substitution
Vector
\(a\cdot b+c\cdot d=(a,c)\cdot(b,d)=\left\lvert(a,c)\right\rvert\cdot\left\lvert(b,d)\right\rvert\cdot cos\theta\)
Exercise 1
\(\sqrt{1-x}+2\sqrt{x}\) max
Cauchy–Schwarz inequality
\((\bar a\cdot\bar b)^2\leq\left\lvert\bar a\right\rvert^2\cdot\left\lvert\bar b\right\rvert^2\)
\(x_1x_2+y_1y_2\leq\sqrt{(x_1^2+y_1^2)(x_2^2+y_2^2)}\)
Exercise 1
\(x+2y+3z=3\) Solve \(\sqrt{x}+\sqrt{y}+\sqrt{z}\)