A mother brings her 8 week old child in for an examination a…

A mother brings her 8 week old child in for an examination and says, “My daughter rolled over against the wall, and now I have noticed that she has this spot that is soft on the top of her head. I think there is something wrong.” What is the nurse’s best response?

You are herding frugs up a trail on a hill (coincidentally,…

You are herding frugs up a trail on a hill (coincidentally, the hill is shaped like a perfectly round paraboloid). As you reach the most south-western part of the mountain trail the evil wolf Eerg appears and chases some of your frugs up the trail! Luckily, you know a shortcut. Write a vector (with numbers for full credit) that describes the direction you go to beat Eerg to the top and recollect your frugs. For the sake of this problem, let’s assume you run just as fast, regardless of the incline. The answer doesn’t depend on the equation for the mountain, but if you would like an example just use f(x,y)=25-x2-y2f(x,y)=25-x^2-y^2 and the points (-3,-3)(-3,-3).

Let SS be the plane 5x+3y-3z=155x+3y-3z=15 in octant V with…

Let SS be the plane 5x+3y-3z=155x+3y-3z=15 in octant V with a downward facing Normal, and F→=\vec{F}=.a) Evaluate ∫S∫(∇×F→)∙N→ dS\int_S\int{(\nabla\times\vec{F})\bullet\vec{N}\ dS}b) Find ∫CF→∙ dr→\int_C{\vec{F}\bullet\ d\vec{r}} where CC is the boundary curve of SS.Hint: it iS possible to answer This part (b) withOut showing any worK as long as you statE why/what theorem(s) you are uSing