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Check the local invertiblity of the function defined by f(x,y)= (x^2- y^2, 2xy) at (-1,1). Find the domain
for the function f in which f is invertible.
1. Use the Squeezing Theorem to show that
lim
X approaches to +sum to infinity
Sin x divide by x =0
2. Use the result in part 1. to find
lim
X approaches to +sum to infinity
Cos πx divide by square root of xsquared +x sinx
Use the Squeezing Theorem to show that
lim
X approaches to +sum to infinity
Sin x divide by x =0
welch construction has found that the value of the company tractor is decreasing at a rate give by v(t)= -390te-0.012t^2, where t represents the number of years after purchase. if the company purchased the tractor for $17650, what is the value of the tractor 3 years after purchase
A company's profit function, in dollars, is given by P(x)= -0.3x^2+56.16x-638 where x is the number of items sold. in addition, the company has a marginal revenue function of MR(x)= -0.6x+76.16. determine the total cost for the company to produce 10 items .
Consider the 3–dimensional vector field F defined by F (x, y,z) = 12x2y2 +2z2 +1, 8x3y −3z, 4xz −3y −3.
(a) Write down the Jacobian matrix JF (x, y,z).
(b) Determine the divergence div F (x, y,z). (c) Determine curl F (x, y,z). (d) Give reasons why F has a potential function.
(e) Find a potential function of F.
Consider the R2 −R function f defined by f (x,y) = xy and let C be the contour curve of f at level 4.
(a) Find a Cartesian equation for the tangent L to C at (x,y) = (1,4).
(b) Sketch the contour curve C together with the line L in R2.
(c) Find an equation for the tangent plane V to the graph of f at (x,y) = (1,4).
Consider the surface S=(x,y,z)∈R3|x2+y2+z2=9.
(a)Define an R3−R function f such that S is the contour surface of f at level 9.
(b)Find an equation for the plane V that is tangent to S at the point (x,y,z) = (2,1,2).
(c) Sketch the surface Sin R3,together with a section of the plane V to illustrate that V is tangent to S at the point (2,1,2).
Find the extreme values of f(x,y)=x^2+y on the surface x^2+y^2=1
A 20 kg weight is attached to the lower end of a coil spring suspended from the ceiling, the spring constant of the spring being 8 N/m. The weight comes to rest in its equilibrium position. Beginning at t=0 an external force given by F(t) 20tan(2t) is applied to the system. Find the displacement in terms of t. Provided that the acceleration due to gravity g=10m/sec2 and has a negligible damping force in the system.
