Behaviour being used: Adaptive mode
Minimum fraction: 0
Question summary: Let [f colon real numbers squared rightwards arrow real numbers] be the function defined by [Error converting from MathML to accessible text.] and the vector [Error converting from MathML to accessible text.] Choose the true statement : The directional derivative of [f left parenthesis x comma y right parenthesis] in the direction of [v equals open parentheses u comma w close parentheses] at the origin is 5·u^2/w; The function is continuous at the origin because there exists the directional derivative at the origin in any direction; The function is diferentiable since the partial derivatives at the origin are continuous; Since [large lim for table row cell left parenthesis x comma y right parenthesis rightwards arrow left parenthesis 0 comma 0 right parenthesis end cell row cell y equals 0 end cell end table of f left parenthesis x comma y right parenthesis equals large lim for table row cell left parenthesis x comma y right parenthesis rightwards arrow left parenthesis 0 comma 0 right parenthesis end cell row cell y equals kx end cell end table of f left parenthesis x comma y right parenthesis equals 0] the function is continuous at the origin; The function is not continuous at the origin despite having directional derivatives in any direction
Right answer summary: The function is not continuous at the origin despite having directional derivatives in any direction
Question state: todo