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1 sketch the curve given by the following and indicate orientation using arrowrrarrt ltnbsp cos t -3 sin t 2tgt2 find
assume that for a certain product its price function of demanding is px 25 - 003 x where x is the quantity of the
1 a curve c is given by the vector equation rt2 - t 3 2t 3ta find the length of the curve in the interval 0 le t le
assume that a ball is expanding in the speed ot 60 cubic centimeters pet minute what is the rate of its radius change
a stone is thrown into a body of calm water sending out a series of concentric ripples if the radius of the outer
consider figure below you will notice that this hyperbolic paraboloid has the equation z x22 - y32 x24 - y29 for
the 12 inch base of a right triangle is growing at 3 inches per hour and the 16 inch height is shrinking at 3 inches
1 let fx frac14 x3 4a sketch a graph of y fx and explain why f is an invertible functionb let g be the inverse of f
1 suppose that fx and gx are differentiable functions and that the following information about them is
consider the surface described by the equation z x3 - zy 3y2i find the equation of the tangent plane to the surface
1 evaluate the limit limisrarr0 sint1 1x23 dx2 write the statement about an improper integral that you have derived in
find the angle between the vectorsfind the equation of the plane in r3 which passes through the three points 1 1 1 4 2
for the series n1sigmainfin1 find a formula for the partial sums sn the limits limnrarrinfin an and limnrarrinfin sn
consider the function fx -14 - 9x2 in what follows h is a formal variableexpress f10 h as a polynomial in hthe
suppose you need to know an equation of the tangent plane to a surface s at the point p2 1 3 you dont have an equation
use the suggested u to find du and rewrite the integral in terms of u and du then find an antiderivative in terms of u
1 draw a contour map of the function fx y radic4x2 y2 draw level curves for z 01242 convert the rectangular point x
given a series rl circuit where vt 10 sin 60pit volts r 1 omega and l 50 times 10-2h find the expression for the
we have worked to make sense of the fact that dsin x dx cos x and d cos x dx - sin x however we have done so with
a mass on a spring vibrates horizontally on a smooth level surface see the figure its equation of motion is xt 4 cos t
a real estate office handles a 60-unit apartment complex when the rent is 530 per month all units are occupied for each
1 given vs 6 s s 22 compute the partial fractions and find the inverse transform using the transform table2 given vs
a light shines from the top of a pole 5 m high a ball is dropped from a point 4 m away from the pole find how fast the
1 use the precise definition of the limit to show that limxrarr2 xx - 1 22 we claim that the equation tan xx 32 has
a cone of radius 2 cm and height 5 cm is lowered point first into a tall cylinder of radius 7 cm that is partially