Question
Calculus Question on Partial derivatives
f(x,y)=\left\\{\begin{matrix} 1-cos(\frac{x^2}{y^2}) \\\ \sqrt{x^2+y^2} \end{matrix}\right. ;if y≠0 & n∈R, then
A
Directional derivatives of f exist at (0,0) & equal to 0.
B
f is continuous at (0,0) but f is not differentiable at (0,0).
C
Partial derivatives of f exist at (0,0) of equal to o.
D
f is differentiable at (0,0).
Answer
f is continuous at (0,0) but f is not differentiable at (0,0).
Explanation
Solution
The correct option is (B,C) :
f is continuous at (0,0) but f is not differentiable at (0,0).
Partial derivatives of f exist at (0,0) of equal to o.