Calculus 3 Exam 1 Review Question and answers verified to pass 2025

Calculus 3 Exam 1 Review Question and
answers verified to pass 2025
Equation of the plane: Given point (x0,y0,z0) and normal vector <a,b,c>. -
correct answers a<x-x0> + b<y-y0> + c<z-z0> = 0


Equation of the plane: Given 3 points P, Q, and R. - correct answers P-Q= PQ
and P-R=PR, then cross multiply to get i,j,k, and then mulitply that vector
times point p to get i<x-x0> + j<y-y0> + k<z-z0> = 0


Chain Rule: Given a set of equations. - correct answers Make a tree and
multiply down until the variable is hit.


Implicit Differentiation: Given an equation. - correct answers dy/dx = -Fx/Fy


Directional Derivative: Given an equation, a point, and a direcion. - correct
answers Find the gradient, plug in the point given, and multiply times the unit
direction.


Tangent Plane: Given equation and point. - correct answers Find the gradient,
plug in point given to get coefficients, and use equation of a plane to get the
tangent plane.


Linear Approximation - correct answers Find the gradient and plug in the
values of the point. Then use equation L=fx(x-a)+fy(y-b)+f(a,b).