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1. Find the linearization of f(x) = 5/√(1-x) at x = 0.
2. Use differentiation to approximate the maximum error in using 5 cm as the radius of a sphere to calculate its volume if the measurement is off by at most 6 mm. Find the approximation of both the relative and percentage error for the volume.
3. Suppose that fluid is leaking from an overhead pipe and spreading in the shape of a circle on the ground. If the radius of the circle is increasing at a rate of 0.5 feet per minute, how fast is the area of the circle increasing when the radius is 3 feet?
4. A road running north to south crosses a road going east to west at the point P. Car A is driving north along the first road, and car 8 is driving east along the second road. At a particular time car A is 10 kilometers to the north of P and traveling at 50 km/hr, while car 8 is 15 kilometers to the east of P and traveling at 80 km/hr. How fast is the distance between the two cars changing?
5. Find the maximum and minimum values of f(x) = x/x2+25 on [0, 10].
he above problem # 1 and find the value of s that makes the area of the pen a maximum
explain dupont analysis and then work through the followingin the year 2007 the average firm in the sampp 500 index had
1. At what interest rate will it take $3000 to grow to $24,000 in an account that earns interest compounded monthly for 20 years? 2. Alice invests $10,000 in an account that earns 8% simple interest annually. What is the value of the account after..
Find a hyperbolic rigid motion that transforms the bowed geodesic from (-4,0) to (2,0) to the bowed geodesic from(10,0) to (20,0)?
Whether or not you win the contract. Put a 1 in the win/lose cell if you win and a 0 in the win/lose ell if you lose.
For the region bounded by y =2x2, y = 8, 0 ≤ x ≤ 2, please Sketch the region. Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region about the y-axis.
the sides AB and BC of the right angle in triangle ABC,inscribed in the circle with centre O,measure 14cm and 48cm respectively. calculate the area of the shaded region?
Your final project entails systematic extraction of decision-aiding insights from a dataset (SampleDataSet.xlsx) provided to you in the Doc Sharing area. The goal of this project is to provide you with hands-on experience in conducting and interpr..
find the volume of one of the smaller wedges cut from a sphere of radius 27 by two planes that intersect along a diameter at an angle of pi/6.
The angular velocity after 2 seconds.
A woman walks due west on the deck of a ship at 2 mi/h. The ship is moving north at a speed of 15 mi/h. Find the speed and direction of the woman relative to the surface of the water. (Round your answers to one decimal place.)
When the surface temperature is 27°C, and decreases by 3°C for every 25m, a sea trout is found at a depth of 150m. If Eleanor wants to put a sea trout in a fish tank, what temperature should she set the sea trout tank to?
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