4) For the function p = x2y+ yz at the point (1,2,-1), find its rate of change with distance in the direction d = i + 2j + 3k. At this same point, what is the greatest possible rate of change with distance and in which direction does it occur? %3D V. (ỹ × 6)

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Q: Find the maximum rate of change of the function f(x,y) = sin (xy) at the point (4,0) and the…

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Q: 3. If f (t) = -t + 5t + 3, describes the distance that a ball has traveled in meters, what is the…

A: We are allow to solve only one question at a time  Thank you for your question

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Q: Two commercial airplanes are flying at an altitude of 40,000 ft along straight-line courses that…

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Q: For the graph y = f(x) = 3x² – x + 2 (i) (ii) Q3. %| - Find the average rate of change of y w.r.t x…

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Q: A square with side x cm, is changing with time where x(t) = 4t – 2. What is the rate of change of…

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Q: A 5-foot-tall woman walks at 7 ft/s toward a street light that is 20 ft above the ground. What is…

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Q: Suppose the position function of a moving object is given by s (æ) = Væ. Then the average velocity…

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Q: Two ships leave port at the same time t = 0. Ship A travels East at km/hr while ship B 2 heads…

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Q: 3. If the temperature in a room is given by T(x, y, z) = xyz, at what rate will the temperature felt…

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Q: Show that for an object falling according to Galileo’s formula, the average velocity over any time…

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Q: The temperature at point (x, y) is given by T(x, y) = 100 – 3x² – y³. Find the direction from point…

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Q: 5. Find the rate of change of the distance D between the origin and a moving point on the graph dx…

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Q: The radius of a star(spherical) was r=a and was observed to increase by 0.01%. Use a linear…

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Q: 8. An express train reducing its velocity to 40 km./h. , has to apply the brakes for 50 sec. . If…

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Q: Martin is inflating a balloon. For a balloon of radius r, the volume is V = 4/3pi(r)2. At the moment…

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A: Solution:-

Q: The rate of change of y is proportional to y. When t = 0, y = 2, and when t = 2, y = 4. What is the…

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Q: The velocity function (in meters per second) is given by v(t) = t2 - 2t - 3, for a particle moving…

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Q: The velocity function of a particle moving along a horizontal line is given by v(t) = ln 2 · 23t,…

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Q: Q. Find the rate of change of z = In Vx² + y² at (3, 4, In 5), (a) In the direction of the positive…

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Q: Find the rate of change f(x, y) = In(2a² + 5y2) at (v2, v2) in the direction making a (positive)…

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Q: 3. If f (t) = -t² + 5t + 3, describes the distance that a ball has traveled in meters, what is the…

A: Given : The function ,ft=-t2+5t+3 describes  the distance travelled by the ball in meters. To find:…