Math 2200 Homework 6 (Finish by: Friday October 29)
Remember to show your work!
Problem 1 Two planes are parallel if they fail to intersect. Find the tangent plane to the
sphere x2 + y 2 + z 2 = 6 at (1,-2,1). Find another point of tangency so that the ta
Math 2200 Homework 5 (Finsh by Friday Oct. 22)
Problem 1 Find the domain and range of f (x, y ) =
xy +1
.
(y 2x+2)1
Problem 2 Find the tangent plane to
f (x, y ) =
2x + 3y
x2 + y 2
at x = 1, y = 1 and also at x = 3, y = 2.
Problem 3 Suppose that f (x, y )
Math 2200 Homework 4 (Due: Friday October 15rd)
Problem 1 For f (x, y ) = x2 Sin(y ) verify that fxy = fyx by taking the partial
derivatives in both orders.
Problem 2 Find the domain and range of each of the following functions.
(i) f (x, y ) = Ln(2x + y
Math 2200 Homework 3
Problem 1 Compute the radius and interval of convergence for
(2x)n .
f (x) =
n=0
Problem 2 Compute the radius and interval of convergence for
f (x) =
(2x)n
.
n
n=1
Problem 3 Compute the McClaurin series for
f (x) = Sin(2x).
Problem 4
Math 2200 Homework 2
Problem 1 Match the following series with properties that they have so that every series matches a property. Some series may match more than one property - which means you may need to shift a matching
to make the entire problem work.
Math 2200 Problem Set 1
Problem 1 Either show that the following sequences fail to converge or show they converge. When
possible, compute their limit. Hint: only one diverges and, of the other ve, four have easily
computed limits. Assume n starts large en
Math 2200 Homework 8 (Complete by Friday November 19th)
Remember to show your work!
Problem 1 Sketch the area D bounded by y = xn and y = xn+2 if n is even. Compute
volume over this region and under f (x, y ) = x + y + 2
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Math 2200 Homework 7 (Complete by Friday November 12th)
Remember to show your work!
Problem 1 Suppose that p(x) is an nth degree polynomial, nd a general formula for
p(x) ex dx
Solution: Let U = p(x), dV = ex dx then dU = p (x)dx and v = ex so
p(x) ex dx
Math 2200 Homework 6 (Finish by: Friday October 29)
Remember to show your work!
Problem 1 Two planes are parallel if they fail to intersect. Find the tangent plane to
the sphere x2 + y 2 + z 2 = 6 at (1,-2,1). Find another point of tangency so that the ta
Math 2200 Homework 5 (Finish by Friday Oct. 22)
Problem 1 Find the domain and range of f (x, y ) =
xy +1
.
(y 2x+2)
Solution: Since this is a ratio of polynomials the only possible problem is a divide by zero so the
domain is the plane less the line where
Math 2200 Homework 4 (Due: Friday October 15rd)
Problem 1 For f (x, y ) = x2 Sin(y ) verify that fxy = fyx by taking the partial
derivatives in both orders.
fx = 2x Sin(y )
fxy = 2x Cos(y )
Solution:
fy = x2 Cos(y )
fyx = 2x Cos(y )
Problem 2 Find the dom
Math 2200 Homework 3 Key
Problem 1 Compute the radius and interval of convergence for
(2x)n .
f (x) =
n=0
Solution: use the ratio test:
Lim (2x)n+1
= |2x| < 1
n (2x)n
1
1
1
So |x| < 2 and the radius of convergence is r = 2 . Plugging in 2 for x to check t
Math 2200 Homework 2 Key
Problem 1 Match the following series with properties that they have so that every series matches a property. Some series may match more than one property - which means you may need to shift a matching to
make the entire problem wo
Math 2200 Problem Set 1 Key
Problem 1 Either show that the following sequences fail to converge or show they converge. When possible, compute
their limit. Hint: only one diverges CORRECTION: 2 diverge and, of the other ve, four have easily computed
limits
Math 2200 Homework 8 (Complete by Friday November 19th)
Remember to show your work!
Problem 1 Sketch the area D bounded by y = xn and y = xn+2 if n is even. Compute
volume over this region and under f (x, y ) = x + y + 2
Problem 2 Sketch the area D bounde
Math 2200 Homework 7 (Complete by Friday November 12th)
Remember to show your work!
Problem 1 Suppose that p(x) is an nth degree polynomial, nd a general formula for
p(x) ex dx
Problem 2 Compute:
3
3
3
3
Problem 3 Compute:
4
2
x2 + y 2 dxdy
Ln(y ) x2 + 1