### Limit - What is the limit of f(x) as x approaches positive and negative infinity where f(x) = (x^3)*e^(-x)?imit -

What is the limit of f(x) as x approaches positive and negative infinity where f(x) = (x^3)*e^(-x)?

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What is the limit of f(x) as x approaches positive and negative infinity where f(x) = (x^3)*e^(-x)?

State the intervals on which the function is continuous (see attached graph)

Please show detailed steps of how to differentiate the following. .. [See the question file for full description.]

Please show detailed steps of how to evaluate the following integrals. Please use natural log. [See the question file for full description]

Find y prime {See Attachment}

I found that the unit cost of using production equip. is: cost = 1.5x(2)[that is to the 2nd power] - 120x + 4,000 where x is the number of units produced. Draw a graph to find the lowest unit cost. what production level does this correspond to?

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See attached file Write a Riemann sum and then a definite integral representing the volume of the region, using the slice shown. Evaluate the integral exactly.

Please help me in attached problems. A customer ordered a quadratic metal sheet with side length x0=10cm. What is the maximal acceptable error of the side length if the area of the metal sheet should be?... For each of the following functions: state if the function is monotone Decide if it is injective, surjective or bij

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A leaky cylindrical oil can has a diameter of 4 inches and a height of 6 inches. The can is full of oil and is leaking at a rate of 2 in.^3/hr. The oil leaks into an empty conical cup with a diameter of 8 in. and a height of 8 in. A. At what rate is the depth of the oil in the conical cup rising when the oil in the cup is 3 in

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1.see attached 2. The amount of alcohol in the bloodstream,A, declines at a rate proportional to the amount, that is dA ____= -kA. If k= 0.6 for a particular dt person, how long will it take for his alcohol concentration to decrease from 0.10%

Please see attachment Find the maximum of...over the closed unit disc.

A pilot, attempting to fly from Middletown to Westburg, a distance of 200 miles, notices after flying 180 miles that West burg is still 35 miles away because the heading was off by a few degrees. How many degrees was the heading off the desired course (to one decimal place)?

Mike, who is standing on the deck of a yacht that is traveling due west at 6km/h, sees a sailboat sailing southwest at 4km/h, 3 km northwest of the yacht. How close to each other do these boats get?

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A survey of college sophomores showed that 5/6 of the males were taking a mathematics class and 3/4 of the females were taking a mathematics class. One-third of the males were enrolled in calculus, and 1/5 of the females were enrolled in calculus. If just as many males as females were surveyed then what fraction of the surveyed

File attached

Find a parametric representation for each of the surfaces. 1.) The part of the sphere x^2 + y^2 + z^2 = 4 that lies above the cone z= square root of x^2 + y^2 2.) The part of the cylinder x^2 + z^2 = 1 that lies between the planes y= -1 and y= 3

Please see attached page for problem. From a plot of F guess whether it is conservative. Then determine whether your guess is correct.

1 of 25 sin -1θ = arc cos arc sin cotangent This is an undefined operation. (All questions are in the attached file.)

Find the area of the region enclosed by one loop of the curve. r = 6sin(11*theta)

See attached file. The relationship between the weight of a child (w, in pounds) and the child's blood pressure (P, in millimeters of mercury) is given by the function above. a. Find the rate of change of blood pressure with respect to weight when the child's weight is 60lbs. b. Find the weight (to the nearest pound)

For x an element of R upper k and y an element of R upper k define d1 (x, y) = max{|x of i - y of i| : 1≤i≤k} and d2 (x, y) = min{|x of i - y of i| : 1≤i≤k}. Determine for each of these whether it is a metric or not. Fully explain your answers. Thank you so much.

The Cartesian coordinates of a point are given. Find the polar coordinates (r,theta) of the point, where r > 0 and 0 less than or equal to theta < 2pie points are (-1, square root of 3)

Please see the attached file for the fully formatted problems.

Please see the attached file for the fully formatted problems.

Eliminate the parameter. Find a rectangular equation for the plane curve defined by the parametric equations. x = 3t, y = t + 7 y = 3x + 7 y = x/3 + 7 y = x/3 - 7 y = 3x - 7 Find a set of parametric equations for the rectangular equation: y = 2x - 2 x = t/2; y = t - 1 y = 2t; 2x = t + 2 y = 2t2 -

Theorem: Suppose that a sequence S of real numbers has a subsequence that converges to a real number a. Then S converges to a. I know this is true as an if and only if statement, but I need a counter example to show that just one converging subsequence isn't enough. Here are two sequences I'm considering: {1,-1,1,-1,1,-1..