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sketch the circle of radius 1 centered at the origin and the circle of radius 1 centered at the point 10 both on the
a write an integral for the arc length of the curve y 25radic25-x2 from x 0 to x 5 you need not evaluate the
find the critical points of the function and determine whether the critical point is a local minimum or maximum or
let a and k be two positive constants find the constants find the center of mass of the solid bounded below by the cone
consider the iterated triple integraly-2int2x0int4-yxz0inty23y2 z2 dz dx dya write down an equivalent iterated triple
let fxy xy then define the vector field frarrxy nablararr fxy sketch the vector field frarrxy by drawing vectors at
at 100 pm ship a is 100 miles due south of ship b if ship a is soiling west at a rate of 14 mph and ship b is sailing
problem descriptiona hospital wants to analyze the performance of its emergency department ed and is interested in the
rlc series circuit in the study of an electrical circuit consisting of a resistor capacitor inductor and an
one way to define hyperbolic functions is by means of differential equations consider the equation y - y 0 the
evaluate the following double integral by using polar coordinatesi intintd 1 - x2 - y2 dawhere the region d is the
consider the double integrali intintd radicx dawhere the region d in the xy plane is bounded by the parabolas x
use poiseuilles law to find the ratio of final blood pressure to initial pressure in an artery where the radius of the
1 a check that y frac12x2 x 3 satisfies the differential equation dydx x 1b check that y sin t satisfies the
two roads meet perpendicularly at an intersection a truck is driving south towards the intersection at 20 meters per
bank robberies the number of bank robberies in the united states for the years 2000-2009 is given in the following
an airplane is f lying horizontally at a speed of 500 mph at an elevation of 10000 feet toward an observer on the
let a and k be two positive constants find the centre of mass of the solid bounded by the cone z2 x2 y2 and above by
consider the iterated triple integraly-2int2 x0int4-y2 z0inty23y2 z2 dzdx dya write down an equivalent iterated triple
a particle moves according to a law of motion s ft 0 le t le 6 where t is measured in seconds and s in feetft
find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and
a cylindrical water tank has height 8 m and radius 2 ma if the tank is full o f water how much work is required to pump
for fxy x3 - y3 xy answer the followinga nablaf1 -2b find the directional derivative of the function f at the point 1
figure shows the velocity of a car during a 5 hour tripa estimate how far the car traveled during the 5 hoursb at what
consider the differential equationdydx -12y1 t2answer the following questionsa is this equation linear or non-linearb