Find the area of the region bounded by the following graphs: y=x^2 ; y=8-x^2 ; and y=x^2+6. I first figured out the area of (8-x^2) minus (x^2) using integral from -2 to 2 and found 64/3 . Then I figured out the area of (8-x^2) minus (x^2+6) using integral -1 to 1 and found 4. I then just subtracted these two regions fr
Please see the attached file for the fully formatted problems. 14) A power plant generates electricity by burning oil. Pollutants produced as a result of the burning process are removed by scrubbers in the smokestacks, Over time, the scrubbers become less efficient and eventually they must be replaced when the amount of pol
Find the linearization, L(x) of f(x) at x = -7 f(x) = sqrt(x^2 + 15).
Which equilibria is stable and which is unstable? Please see attached file for full problem description.
Please see the attached file for the fully formatted problem. The equation x2 - 3x + 1 = 0 has a solution for x>= 0. Give the third approximationby using Newton's method. Your first approximation is to be 1.
Y=2*sqrt[x] y=0, x=3 We are using the following formula 2pi intergal of r(x) times the sqrt of 1 + (f'(x))^2.
Please see the attached file for the fully formatted problems. Questions pertain to Second order Taylor approximations and integrals for two first order differential equations.
Prove that if x>0, then 1+x/2-x^2/8<(1+x)^(1/2)<1+x/2
Define: f(x) = (x^2)sin(1/x)+x if x doesn't equal 0 f(x) = 0 if x=0 Prove that the function f:R-> R is differentiable and that f'(0)=1. Also prove that there is no neighbourhood I of 0 such that the function f:I->R is increasing.
Sum of a series
Evaluate f(1,2) and f(1.05, 2.1) for the function Æ'(x,y)=x/y. a) calculate Δz b) use the total differential dz to approximate Δz
You are given the function w=yz/x, where x=θ^2, y=r+θ and z=r-θ. Find ∂w/∂θ. a) using the appropriate chain rule b) converting w to a function of r,θ before differentiating. Which of the above is quicker?
A metal plate is located in an xy-plane such that the temperature T at (x,y) is inversely proportional to the distance from the origin, and the temperature at point P(3,4) is 100 (i.e. the temperature at any point (x,y) is described by the function T(x,y) = 500/(x^2 + y^2)^1/2 a) in what direction does
Describe the level curves of the function. Sketch the level curves for the given values of c. f(x,y) = x^2 + 2y^2, c = 0,1,2,3,4
Describe projection on the x-y plane ( center, radius)
Please see the attached file for the fully formatted problems. Use the formulas to set up an integral for the surface area of the first octant portion of the sphere p=a, do not evaluate. See attachment
Please see the attached file for the fully formatted problems. Let be a sequence of real numbers. We define and I'm having trouble with the following three proofs: 1) Show that 2) Show that if the limit of only exists when , then . 3) Show that if , then the limit exists, and .
Please answer eight (8) calculus problems. Please show as much works as possible for every problem. The problems are posted in the following website: http://www.netprofitspro.com/math.html
Let I be an open interval and n be a natural number. Suppose that both f:I->R and g:I->R have n derivatives. Prove that fg:I->R has n derivatives, and we have the following formula called Leibnitz's formula: (fg)^n(x) = the sum as k=0,1,2,...n of(n choose k)f^k(x)g^(n-k)(x) for all x in I. Write the formula out explicitly
Show that the volume enclosed by the surface ___ is equal to ___. Please see the attachment.
Please see the attached file for the fully formatted problem. Show that the average distance of a point of a disk with radius a is...
Please see the attached file for the fully formatted problems. Find the volume and centroid of the ice cream cone.
Please see the attached file for the fully formatted problem. Find the mass and centroid of a plane lamina with the given shape and density delta, the region bounded by y = x2 and x = y2 delta(x,y) = x2 + y2.
Give examples of polynomials of degree 3 that have no critical point, only one critical point, and two critical points.
If I be an open interval containing the point x. (x0) and suppose that the function f:I->R has two derivatives. Prove that lim as h->0 (f(x.+h) - 2f(x.) + f(x.-h))/ h^2 = f"(x.)
The inverse cosine function has domain [-1,1] and range [0, pi]. Prove that (cos^-1)'(x) = -1 / sqrt(1-x^2)
Find dy/dx implicitly: x^2+6xy-5y+y^3=12
A ball is dropped from the top of a building which is 1000 feet tall. GIVEN (s(t)=-16t^2+v(initial)t+s(initial)) A. Write the position and velocity functions for the ball. B. Find the instantaneous velocity went t = 2 seconds. C. How long does it take the ball to reach the ground. Please solve using calculus (derivativ
Find the equation of the line tangent to the graph of f(x)=x^3+x at the point (-1,-2).
Find the points at which the function has a horizontal tangent line. f(x)=x^2+4x+5