Q60Multiple correct3 Marks11 Dec 2022

Which of the following options is/are true?

A

z = 3x + e^2 * y - 2 - e^2 is the tangent plane to the function u(x, y) at point $(1, 2)$.

B

x(t) = 1 + (1/sqrt(2)) * t, y(t) = 2 + (1/sqrt(2)) * t, z(t) = (1 + e^2) + (1/sqrt(2)) * e^2 * t is the tangent line of the function u(x, y) at point $(1, 2)$ in the direction of (1/sqrt(2))(1, 1).

C

z = 2e*x + (1 + e)*y + 4 - 3e is the tangent plane to the function v(x, y) at point $(1, 2)$.

D

x(t) = 1 + (1/sqrt(2)) * t, y(t) = 2 + (1/sqrt(2)) * t, z(t) = (8 + 2e) + (12 + 3e)/sqrt(2) * t is the tangent line of the function v(x, y) at point $(1, 2)$ in the direction of (1/sqrt(2))(1, 1).