(a) If $u(x,y) = \log\left(\frac{x^2+y^2}{xy}\right)$, then prove tha…

Question

(a) If $u(x,y) = \log\left(\frac{x^2+y^2}{xy}\right)$, then prove that $\frac{\partial^2 u}{\partial x \partial y} = \frac{\partial^2 u}{\partial y \partial x}$.

(b) State Lagrange's Mean Value theorem and verify it for the function $f(x) = \sin x$ in $\left[0, \frac{\pi}{2}\right]$.

(c) Using Lagrange's method of undetermined multipliers, find the maximum value of $\cos x \cos y \cos z$ given that $x + y + z = \pi$.

Related pages

• Lagrange's Multipliers — topic
• Engineering Mathematics-I syllabus