Question

(A) Assume that *x* and *y* are functions of
*t*. If y = x^{3} + 6x and dx/dt = 5, find dy/dt
when x = 3.

dy |

dt |

= ?

(B) Assume that *x* and *y* are positive functions
of *t*. If x^{2} + y^{2} = 100 and dy/dt =
4, find *dx/dt* when y = 6.

Answer #1

(part a) Assume that x and y are positive functions of t. If x2
+ y2 = 100 and dy/dt = 4, find dx/dt when y = 6.
(part b) Suppose x, y, and z are
positive functions of t. If z2 = x2
+ y2, dx/dt = 2, and dy/dt = 3, find dz/dt when x = 5
and y = 12.

dy/dt=x , dx/dt=6x-8y, x=1 and y=-1 when t=0

Consider the following. y = 6x^4 − 5x − 1/4 − x^2
A)Find the value of y when x = 1.
y(1) =
B Find dy/dx .
dy/dx =
C Find the exact value of dy/dx when x = 1.
dy/dx =
D Write the equation of the tangent line to the graph of y = 6x4
− 5x − 1 4 − x2 at x = 1. Check the reasonableness of your answer
by graphing both the function and...

1) Solve the given differential equation by separation of
variables.
exy
dy/dx = e−y +
e−6x −
y
2) Solve the given differential
equation by separation of variables.
y ln(x) dx/dy = (y+1/x)^2
3) Find an explicit solution of the given initial-value
problem.
dx/dt = 7(x2 + 1), x( π/4)= 1

Assume that (X, dX) and (Y, dY ) are
complete spaces, and give X × Y the metric d defined by
d((x1, y1),(x2, y2))
= dX(x1, x2) + dY
(y1, y2)
Show that (X × Y, d) is complete.

a. *If
y=x3+7/x^2/3
, then find dy/dx . Make sure your answer is
fully simplified.
b. *If y=5x-84x+3 , then
find dy/dx .
c. *If
x=(x2-5x+3)(2x2+4)
, then find f ‘(x).
Please neatly show your work.

solve the given initial value problem
dx/dt=7x+y x(0)=1
dt/dt=-6x+2y y(0)=0
the solution is x(t)= and y(t)=

Please show all steps, thank you!
a) Verify that the functions below solve the system:
x(t) = c1e^5t + c2e^-t
y(t) = 2c1e^5t - c2e^-t
Do not solve the system
dx/dt = x + 2y
dy/dt = 4x +3y
b) Solve the system using Operator D elimination. Write the
answer both in scalar and vector form. Please show all steps!
dx/dt = x + 2y
dy/dt = 4x + 3y

a). Find dy/dx for the following integral.
y=Integral from 0 to cosine(x) dt/√1+ t^2 ,
0<x<pi
b). Find dy/dx for tthe following integral
y=Integral from 0 to sine^-1 (x) cosine t dt

1) Differentiate the function
y= 1/ (9x-8)6
2) Find the derivative of dy/dx of the given function
y= x3(2x-9)7
3) Differentiate the function
y=(4x-4)2(2-x5)2
4) Differentiate the given function
y=(x+4/x-9)8
5) Find the indicated derivative
d/dt ((4t-8)5/t+6)

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 3 minutes ago

asked 9 minutes ago

asked 14 minutes ago

asked 15 minutes ago

asked 31 minutes ago

asked 38 minutes ago

asked 52 minutes ago

asked 54 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago