Write-ups due Monday April 18.
Monday
April 10
Solve,
write up and turn in:
1. Consider the function f(x,y) and
let g(t) = f( x0+at, y0+bt
)
(where a,b are numbers).
a. Calculate dg/dt and d^2
d/ dt^2.
b. Write the Taylor polynomial of degree 2 of g at
t=0 and the expression for the remainder.
2. The same
problem for f(x,y,z) and
g(t) = f( x0+at, y0+bt, z0+ct
) .
Wednesday April 12
Solve:
Sec.
19.7: 1, 4
Solve, write up and turn in:
Sec. 19.7:
9a,c, 10, 19, 21
Sec. 19.10: 2, 3, 13, 14
1. Find
the linear approximation at (1,0) for
the function
f(x,y)=the integral from 0 to x of
sin(t^3y^2) dt
2. Complete the squares to show that
fxx/2 x^2 +fxy x y
+fyy/2 y^2 equals
A^2/(2fxx)
+D/(2 fxx) y^2
where D is the
discriminant and A=fxx x+fxy
y.
Thursday April 13
Read
Example 3 p. 700.
Solve, write up and turn in:
Sec.
19.10: 11, 13
Sec.
19.8: 1, 2, 4b (but see Change below) , 17, 19,
20
Friday April 14
Check
out the Exteme
Value Theorem and examples.
Solve,
write up and turn in:
1. Consider the function
f(x,y,z)=x^2+y^2-xz on the
domain
x>0, y>0, z>0, x+y+z<1.
Sketch
the domain and find the absolute maximum and minimum of the function.
2. Consider the
function f(x,y)=1+square root of (4x^2+y^2) on the
domain x^2+y^2<1.
Sketch the graph of the function
and name this surface.
Find the absolute minimum and maximum of
this function on the stated domain.
Explain why absolute extrema
necessarily exist for this function on this domain.
Change:
problem 4b page 701 became a bonus problem worth extra
5 points; you can turn it in now,
or on April 24.