Question

f(x,y)=-e^(3x^2+6y^2)+e^(5y^2+1) identify the shape of
the level curve which contains (-sqrt(3)/3,0)

take as the parallelogram bounded by

x-y=0, x-y=3, x+2y=0, x+2y=2

(9x+3y)dxdy

Answer #1

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find the general solution.
1- y^6(4)+12y''+36y=0
2-6y^(4)+5y'''+7y''+5y'+y=0
3-y^(4)-4y'''+7y''-6y'+2y=0

Verify that the given function is the solution of the initial
value problem.
1. A) x^3y'''-3x^2y''+6xy'-6y= -(24/x) y(-1)=0 y'(-1)=0
y''(-1)=0
y=-6x-8x^2-3x^3+(1/x)
C) xy'''-y''-xy'+y^2= x^2 y(1)=2 y'(1)=5 y''(1)=-1
y=-x^2-2+2e^(x-1-e^-(x-1))+4x

a.) Find the length of the curve y=ln(x),1 ≤ x ≤ sqrt(3)
b.) Using disks or washers, find the volume of the solid
obtained by rotating the region bounded by the curves y^2=x and
x=2y about the y-axis
c.) Find the volume of the solid that results when the region
bounded by x=y^2 and x=y+12 is revolved about the y-axis

The
curve x = sqrt( (2y-y ^ 2) ) with 0 <= y <= 1/2 is rotated on
the y axis. Find the surface area of the solid obtained.

Question 1
What is the vertex of f(x) = x2 + 3x + 2?
Select one:
a. 7
b. (0, 2)
c. (-3/2, -1/4)
d. -3/2
e. None of these
Question 2
What is the exact value of sin (22.5 degrees)?
Select one:
a. .383
b. sqrt (2)
c. sqrt ((2 – sqrt(2)) / 2)
d. sqrt ((2 + sqrt (2)) / 4)
e. Impossible
Question 3
Solve the system: 2x + 3y = 7, 3x - 5y = 1...

Solve the differential equation:
a) y'= t^2y^3 / t^3+6
b) y'= x(e^x^2 +2) / 6y^2 ; y(0) =1

1.
The linearization of f(x)=(e^x^2) at x=1 is?
2. The linear approximation of f(x)=sqrt(x+3) is?
3. compute the average value of f(x)=(x^3)+(3x^2) over
interval [1,2] is?

part 1)
Find the partial derivatives of the function
f(x,y)=xsin(7x^6y):
fx(x,y)=
fy(x,y)=
part 2)
Find the partial derivatives of the function
f(x,y)=x^6y^6/x^2+y^2
fx(x,y)=
fy(x,y)=
part 3)
Find all first- and second-order partial derivatives of the
function f(x,y)=2x^2y^2−2x^2+5y
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 4)
Find all first- and second-order partial derivatives of the
function f(x,y)=9ye^(3x)
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 5)
For the function given below, find the numbers (x,y) such that
fx(x,y)=0 and fy(x,y)=0
f(x,y)=6x^2+23y^2+23xy+4x−2
Answer: x= and...

1) The region bounded by f(x)=−3x^2+18x+21, x=0, and y=0 is
rotated about the y-axis. Find the volume of the solid of
revolution.
Find the exact value; write answer without decimals.
2) Suppose you lift a laptop that weighs 3.2 pounds off the
floor onto a shelf that is 4 feet high. How much work have you
done?
foot-pounds
3) The force on a particle is described by 9x^3−1 pounds at a point
xx feet along the x-axis. Find the work...

consider the funtion f(x)=3x-5/sqrt x^2+1. given
f'(x)=5x+3/(x^2+1)^3/2 and f''(x)=-10x^2-9x+5/(x^2+1)^5/2
a) Find the domain of f. (write in interval notation):
Df:=_____________?
b) Find the x- and y- intercepts. if any. (write your answers as
ordered pairs).
c) Find the asymptotes of f, if any. If there are not, write
why. (write answers as equations).
d) Find all of the critical numbers of f. on what intervals is f
increasing/decreasing?
show all work

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