Please see the attached file for full problem description. (a) By making the substitution y = z/x^4, or otherwise, reduce the equation dy/dx +4y/x =sinx/x2 to an equation in which the variables are separable. Solve the equation if y = 0 when x = pi/2 (b) In a circuit di/dt=K(E-Ri) and i=0 when t=0. Find i in
(A) Find and simplify the difference quotient for G(X)=1/x^2. HINT: After finding the difference quotient, simplify by using an LCD to combine the fractions. (B) Using the answer above, find the value of the difference quotient at x=1 with an h=.1 C) Sketch a graph of G(x). Mark the point(1,G(1)) on the graph. Sketch a
Please see the attached file for the full problem description. 1. (a) If f (r, theta) = r^n cosntheta show that (see attached file) (b) If u = y^3 - 3x^2y prove that (see attached file).
I have a first derivative and a second derivative, how do you get from the first to the second, I can't solve it. Please see the attached file for the fully formatted problems. M'(t) = pe^t/(1 - t^tq)^2 M''(t) = pe^t(1 + qe^t)/(1 - (e^t)q)^3
(a)Find the orthogonal trajectories of the family of curves defined by 2cy + x2 = c2, c>0 State the differential equation of the orthogonal family, and show your steps in obtaining a solution. (b) On the same set of "square" axes, plot at least five members of each of the given family and your family of orthogonal soluti
Suppose that the temperature at the point (x, y, z) in space (in degrees Celsius) is given by the formula: W= 100 - x^2 - y^2 - z^2. The units in space are meters. (a) Find the rate of change of temperature at the point P(3, -4, 5) in the direction of the vector v=3i - 4j + 12k. (b) In what direction does W increase most rapidly
Find the directional derivative of f at P in the direction of v; that is find D_u f(P), where u=v/{v}: f(x, y, z)= ln(1 + x^2 +y^2 - z^2) ; P(1, -1, 1), v=2i - 2j -3k
Write chain rule formulas giving the partial derivative of the dependent variable p with respect to each independent variable: p=f(x, y, z); x=x(u, v), y=y(u, v), z=z(u, v)
Let f be the function whose graph goes through point (3,6) and whose derivative is given by f'(x) = (1+e^(x))/(x^2) a) write the equation of the line tangent to the graph of f at x=3 and use it to approximate f(3.1) b) Use Euler's method, starting at x=3 with a step size of .05 to approximate f(3.1). Use f'' to explain wh
I am taking a course by distance, and my professor provided an example of how to create a Hessian matrix using partial derivatives. He gave another example that just had the solution for us to try on our own. I think that I am somehow not taking the second order partial derivative right. The attached file has the professor
See attached file for full problem description. y = 1/x^4 - 3x^2 + 2x - 1.6
This equation represents displacement of a body(s)against time(t) where (u) is the initial velocity and (a) is the acceleration Differentiate this equation for instantaneous velocity and work out the acceleration of a body from rest to the final velocity if t= 24 secs. and v= 4.01m/s
Let f be a function that is differentiable for all real numbers. The table gives the values of f and its derivative f' for selected points x in the closed interval -1.5<or equal x< or equal 1.5. The second derivative of f has the property that f''(x)>0 for -1.5<or equalx<or equal 1.5 Find a positive real number r having the
A lighthouse is 30 miles off a straight coast and a town is located 25 miles down the sea coast. Supplies are to be moved from the town to the lighthouse on a regular basis and at a minimum time. If the supplies can be moved at a rate of 4 miles per hour on water and 40 miles per hour on land, how far from the town should the do
Find the derivative dy/dx if y = x^(x+3)
The heat transfer in a semi-infinite rod can be described by the following PARTIAL differential equation: ∂u/∂t = (c^2)∂^2u/∂x^2 where t is the time, x distance from the beginning of the rod and c is the material constant. Function u(t,x) represents the temperature at the given time t and p
Find the derivative of the function y=x^2e^(3x) See Attachment for a cleaner version of the question.
Let f be a function given by x + 2 if x < 0 f(x) = x if x >= 0 Is there a function g: R ---> R such that g'=f? *be careful applying definition of the derivative
I want to prove, for the numbers a and b, that the following equation has exactly three solutions if and only if 4a^3 + 27b^2 < 0: x^3 + ax + b = 0, x in R
At what rate is the surface area of a cube changing the edge measures 5 inches and is changing at a rate of 2 in/min. GIVEN (A=6*s^2)
Prove that if f(x) = x^alpha, where alpha = 1/n for some n in N (the natural numbers), then y = f(x) is differentiable and f'(x) = alpha x^(alpha - 1). Progress I have made so far: I have managed to prove, (x^n)' = n x^(n - 1) for n in N and x in R both from the definition of differentiation involving the limit and the binomial
Find partial deriv's w/r and w/theta using appropriate chain rule for : w=the square root of (25-5x^2-5y^2), where x=r cos theta, y= r sin theta.
A) z=y^3-4xy^2-1 B) first partial derivative WRT x,y,z for : w=3xz/(x+y)
Given The Maclaurin series for the inverse hyperbolic tangent is of the form x+x^3/3+x^5/5...x^7/7. Show that this is true through the third derivative term.
Use the product rule find derivative of h(t)= cubed root of t * (t^2+4)
Find the first partial derivative with respect to x, y, z. w = 3xz / x+y
Let f be the function: F(x) 1/4 x=o, x 0<x<1 3/4 x=1 Using standard partition Pn (0,1) where n greater or equal to 4 L(f, Pn) = 2n(squared) -3n+4 all divided by 4n(squared) U(f,Pn) = 2n(squared) +3n+4 all divided by 4n(squared) and deduce that f is intergrable on (0,1) and evaluate (intergral sign with 1 at t
1.) Find the derivative of the function: a.) f(x) = x + 1/x^2 b.) f(x) = (2/3rd root of x) + 3 cos x 2.) Find equation of tangent line to the graph of f at the indicated point: a.) y = (x^2 + 2x)(x + 1) ; (1,6)
The equation for a wave moving along a straight wire is: (1) y= 0.5 sin (6 x - 4t) To look at the motion of the crest, let y = ym= 0.5 m, thus obtaining an equation with only two variables, namely x and t. a. For y= 0.5, solve for x to get (2) x(t) then take a (partial) derivative of x(t) to get the rate of change of
What is the equation of the reversal tangent of the following function: f(x)=-(x^3)+9x^2-(29x)+35