Find the maximum rate of change of the function f(x,y) =4x^2-2y^3 at the point (1,1)

Q: A coat of paint of thickness 0.02 cm is to be applied uniformly to the faces of a cube of edge 21…

A: We know that,

Q: A tin can has a circular base of radius 2 inches and height of 6 inches. If the thickness of its…

A: We have to find the volume of tin can using differentials.

Q: Use forward, backward and centered difference approximations to estimate the first derivative of:…

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Q: A function has a tangential gradient of 2sin3x. If the curve cuts the x-axis at, determine the…

A: A function has a tangential gradient  of 2 sin 3x.If the curve cuts the  x-axis at π3.To determine…

Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.1 cm/min.…

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Q: Water is draining from a cylindrical tank of water at a rate of 3 m / min . If the radius of the…

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Q: Describe the General Power Rule for Integration in your own words

A: The general power rule for integration is: So this means we add 1 with the exponent to get a new…

Q: Explain how a directional derivative is formed from the two partial derivatives ƒx and ƒy.

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Q: volume

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Q: A rectangular shaped region is changing with time and increasing in the x direction at the rate of 2…

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Q: A spherical snowball melts at a rate proportional to its surface area. Show that that rate of change…

A: It is given that, the spherical snowball melts at a rate proportional to it’s surface area. This can…

Q: How can you relate antiderivatives as an opposite of derivatives in your life? explain

A: Solution is given below:

Q: Find total differential of function u = x.

A: 6. The given function is u=xyz. We know that the total differential of a function u=fx,y,z is given…

Q: 4. The organism amoebus rectilineus always maintains the shape of a right triangle whose area is 10°…

A: 4. Consider a right angled triangle: Here, Hypotenuse=hHeight=aBase=b   Given: Area of triangle A…

Q: TOL Company Ltd have undertaken an investigation for a client cor and has discovered that the total…

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Q: Find the maximum rate of change of f (x, y) = xy ^ 2 + root (y) at the point (2,1). in which…

A: The maximum rate of change of f(x, y) happens along the direction grad(f) at the given point (2, 1).…

Q: Use differentials to approximate the increase in the area of a soap bubble when its volume increases…

A: Let the radius of the soap bubble be a cm, then the volume of the soap bubble is: V=43πr3        And…

Q: A particle is moving along the curve y = 2+ Vx + 1. At the instant that the partical passes through…

A: (15) Find dy/dt from y using the chain rule and dx/dt from the statement given.

Q: Assume the accleration of the object is a(t) = −9.8 meters per second per second. (Neglect air…

A: When the ball will reach it's maximum height, at that point of instance the final velocity will be…

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.3 cm/min.…

A: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.3…

Q: A runner starts on the east side of a circular track of radius 300 feet. Let’s say their inital (x,…

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Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min.…

A:

Q: A tank whose volume is 150 L is initially half full of a solution that contains 100 g of chemical. A…

A: Given that, A tank whose volume is 150 L is initially half full of a solution that contains 100 g of…

Q: A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2 cm/min.…

A: Rate of change

Q: an open hemispherical container has radius 20 feet. honey begins flowing into the tank in such a way…

A: Let depth be h. Volume of the honey in the container is:  Also, radius of circular surface is:…

Q: Let u=sinx and the integrand will lead to integration by partial fraction

A: use substitution method for solving the  integral

Q: (b) Use the First Derivative Test to identify all local extrema. Local minimum at x = Local maxiтит…

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Q: 4y4 at the Find the maximum rate of change of the function f(x, y) point (5,1)

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Q: A box with a square base has the sides of the base increasing at  6 m/sec and the height of the box…

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Q: Air is pumped into a spherical balloon at the constant rate of 200 cubic centimeters per second. How…

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Q: When is integrating using the tabular method useful?

A: When is integrating using the tabular method useful?

Q: Determine the Derivative of the Function: 1. y = ex - 1/ex + 1 2. y = x22x 3. y = 43x^2 4. f(x)…

A: Find derivatives

Q: Why is anti-differentiation or integration important in our lives?

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Q: Find all second order partial derivative with respect to variable x and y. F(х,у)- х сosxу + y sinx…

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Q: The population of a city is associated by the function P(x,y,z)=x² + 2y² + 2z². If the population of…

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Q: Water is flowing into a vertical cylindrical tank or radius 2 meters at a rate of 8 cu. meters per…

A: Given that vertical cylindrical tank that has radius 2 meter and water is flowing rate is 8cu.…

Q: Find the indicated partial derivative.

A: Given that, f(x, y) = y sin-1 (x, y) We have to find fy(1, 1/2).

Q: Find the average rate of change of LaTeX: f\left(x\right)\:=3x^2+1 f ( x ) = 3 x 2 + 1 between…

A: Formula for average rate of change is f(b)-f(a)b-a.

Q: What is the reversed order of integration of dydx ?

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Q: A conical tank with the vertex down measures 10 meters in height and 9 meters in diameter of its…

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Q: Find the area of a triangle bounded by lines y=2x and x=1 by single integration

A: A definite integral can be used to compute area bounded by curves. If there are two curves f,g over…

Q: Evalute Sofy ex* dxdy by first reversing the order ex² 3y integration.

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Q: integral of:

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. (x, y)…

A: First find gradient and take magnitude for max rate of change

Q: Find the maximum rate of change of f(r,y) = sin(x + y) at the point (1,-1) and the direction at…

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Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min.…

A: To find the rate of decreasing of the volume when the radius is 10 cm.

Q: A 5 meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder…

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Q: Find the derivative of y. y = 3ztanh (z)+3In /1-z y' = 3 sinhz y' = tanh 3z y' = 3 tanhz y' = 3…

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Q: A stone is thrown vertically upward from a point 1.5 m above the earth’s surface with an initial…

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Exponential Growth Model

The relation that represents an exponential function is: