Let z = g(x, y) = f(3 cos(xy), y + e™v) provided that f(3, 5) = 5, f1(3, 5) = 2, f2(3, 5) = 5. i) Find gi (0, 4). i) Find g2 (0, 4). iii) Find the equation of the tangent plane to the surface z = the point (0, 4). f(3 cos(ry), y + e™") at

Q: Find the point where the tangent line to the curve 7(?) = (V? +3,ln(?² +3),t) at (2, In 4,1) 5. %3D…

A:

Q: Find the tangent plane to the equation z = z = 3x² + y² + 4y at the point (1, 0, 3)

A:

Q: Find an equation, in slope-intercept form, of the line tangent to the curve with parametric…

A:

Q: B) r(t) = (4 cos t, 4 sin t, 16)

A: We consider x=rcos(theta) and  y=rsin(theta)  Therefore r^2=x^2+y^2

Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: 6. Given f(x, y) = 2x³y=x²y³, a) find the directional derivative of f(x, y) at (1, 1) in the…

A:

Q: Consider the function f(r, y) = e=² sin( q² + y²) (a) ) Compute the gradient of f. (b) 1 ) Find the…

A: Given fx,y=e-xsinx2+y2

Q: Find an equation for the tangent plane to the surface x = u² – v², y = u + v, 2 = u² + 4v at (-},2).

A: We have r(u,v) = (u2-v2)i + (u+v)j + (u2+4v)k