Behaviour being used: Adaptive mode
Minimum fraction: 0
Question summary: Let [f comma g colon real numbers squared rightwards arrow real numbers squared] the functions defined by [Error converting from MathML to accessible text.] Let [Error converting from MathML to accessible text.] be the function defined by [Error converting from MathML to accessible text.]. Choose the correct statement (there may be more than one) : Although [f] is differentiable at the origin, his partial derivatives are not continuous; The linear approximation of [G] in a neigbourhood of the origin is [G left parenthesis x comma y right parenthesis asymptotically equal to][[x-4·y],[1]]; [H equals G ring operator G] is differentiable at the origin because [G] is differentiable at the origin; [dH open parentheses 0 comma 0 close parentheses equals # w times # w]; The maximum directional derivative of [f] at the point (1,1) is (109·e^2-24·e+16)^(1/2)/e; The tangent planes at the surfaces [z equals f left parenthesis x comma y right parenthesis] at the origin and [z equals g left parenthesis x comma y right parenthesis] at the point (0,0,1) intersect at the line with equation [Error converting from MathML to accessible text.]
Right answer summary: The linear approximation of [G] in a neigbourhood of the origin is [G left parenthesis x comma y right parenthesis asymptotically equal to][[x-4·y],[1]]; The maximum directional derivative of [f] at the point (1,1) is (109·e^2-24·e+16)^(1/2)/e
Question state: todo