Hello, my name is Peter. I'm currently a rising junior at the University of Notre Dame, majoring in computer science. I have taken and not scored lower than a B in several rigorous university-level math classes, including probability and statistics, linear algebra and differential equations, calculus 3, discrete mathematics, and more. I have been tutoring fellow students at Notre Dame in math and computer science classes for two semesters. I have a passion for explaining concepts that I understand to others who are struggling with the concepts.
(a) Eliminate the parameter to find a Cartesian equation of the curve.(b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.$x=e^{t}-1, \quad y=e^{2 t}$
Write the explicit function $z=x y^{2}+x^{2} y-10$ in the implicit form $F(x, y, z)=0$
Write an equation for the plane tangent to the surface $F(x, y, z)=0$ at the point $(a, b, c)$
Tangent planes for $F(x, y, z)=0$ Find an equation of the plane tangent to the following surfaces at the given points. $$x^{2}+y+z=3 ;(1,1,1) \text { and }(2,0,-1)$$
Tangent planes for $F(x, y, z)=0$ Find an equation of the plane tangent to the following surfaces at the given points. $$x^{2}+y^{3}+z^{4}=2 ;(1,0,1) \text { and }(-1,0,1)$$
Tangent planes for $F(x, y, z)=0$ Find an equation of the plane tangent to the following surfaces at the given points. $$x y+x z+y z-12=0 ;(2,2,2) \text { and }(2,0,6)$$
