Use implicit differentiation to help you find the value of the gradient for the equation x² – e = y(x – 2) + 8 at the point (3,0) and use linear approximation to estimate the value of y when x = 2.98.

Q: function of the radius (r) and the height (h) and is given by V= pi r2h. Determine the two parital…

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Q: a) Find the directional derivative of a(r, y) = 3-y at (1, 1) in the direction (-3,4). b) Find and…

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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: Find the gradient of the function at the given point. z=y/x^2+y^2   (2, 2) Find the maximum value of…

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Q: The method of u-substitution is the integral analog of the chain rule of derivatives and the method…

A: Let say we have two functions f(x) & g(x)Now combine the function f(g(x))Hence, the derivative…

Q: Illustrate local linearity for the function f (x) = xsinx at x = l.

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Q: (b) Apply the First Derivative Test to identify the relative extrema. (x, y) = ( ,1 2 relative…

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Q: Find i) Partial derivative. tii) of the function i Z= 200+xy Level Sur face エエ

A: Given z=200+x2y2 i) Partial derivative zx=0+2xy2=2xy2zy=0+2x2y=2x2y ii) Level surface of the…

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z2 (5,…

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Q: 2b. Explain the difference between a partial derivative and a directional derivative.

A: Dear learner, as per our guidelines we can provide the solution for one part only. Kindly post other…

Q: An orchard has an average yield of 36 bushels of apples/tree if the density is 22 trees/acre. For…

A: Let x be the additional number of trees to be planted to maximize the total yield.

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

A: Solution is given below:

Q: Use implicit differentiation to help you find the value of the gradient for the equation x² – ev =…

A: given equation x2-ey=yx-2+8 claim- use implicit differentiation to help you find the value of the…

Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) 3 x2 + y2 + z2 (7,…

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Q: the profit P for a company is P=100xe-x/400 where x is in sales. use the method of differentials to…

A: As a first step let's find the derivative of P as shown on whiteboard and establish the relationship…

Q: Find the gradient of the function at the given point. Function f(x, y) = x² + 2xy Vf(5,2)= (No…

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Q: How can linear approximation be used to approximate the changein y = f(x) given a change in x?

A: Given;                 y=fx How can linear approximation be used to approximate the changein y=f(x)…

Q: Find the 1st order derivative for    R(x,y) = [(x^2)/(y^2 + 1) ]  -   [(y^2)/(x^2  + y)]

A: Given function is R(x,y)=x2y2+1-y2x2+y Differentiate partially with respect to x.…

Q: Find the gradient of the function at the given point. y Ri (2, 2) x²+ y2' Vf(2, 2) = %3D Find the…

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Q: ди Calculate the partial derivative using implicit differentiation of + y = 6 at (x, y, w) = (1,2,…

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Q: Find the gradient of the function at the given point. Function Point (7,4) f(x, y) = Vf(7, 4) = x +…

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Q: 22. The gradient of the implicit function to the curve x2 + y? = 13 at the point (2, -3) is A B 2 2

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² y2 + z2 (3, 5,…

A: To find the gradient of the function at the point given

Q: Find the gradient of the function: y = (5x ln (x)/ 6) + x/3 at the point with x-coordinate 1. Give…

A: We can solve this problem as follows:

Q: Calculate the partial derivative using implicit differentiation of + = 10 at (x, y, w) = (1,2, 1).…

A: Given query is to find the derivative of the expression.

Q: . Find the average rate of change of y = x' over the interval [1, 3]. Determine the slope of the…

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Q: Find the gradient of the function at the given point. Function Point x + 4y f(x, y) (3, 1) y + 1…

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Q: Compute for the derivative of the function using rules for differentiation. Properly implement the…

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z2 (2,…

A: We have to find maximum value of the directional derivative at the given point.

Q: Determine the gradient of the straight line which is tangent to the graph of f(x)= tan^-1(ln x) at…

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Q: The curve y = 2x² +- k has a gradient of 5 when x 2. Calculate: (а) The value of k. (b) The minimum…

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Q: Calculate the partial derivative using implicit differentiation of x'w + w + wz? + 3yz = 0. (Use…

A: Use the following formulas: 1.∂∂xxn=nxn-12.∂∂x(a.b)=a.∂b∂x+b∂a∂x

Q: The maximum rate of change at a point on a function f(x,y,z) is да ylgr

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Q: Find the gradient of pthe function and the maximum value of the directional derivative at the point…

A: To finds the gradient of the funxction and the maximum value of thedirectioonal derivative at the…

Q: Calculate the partial derivative d using implicit differentiation of x³w+w7+ wz² + 2yz = 0. дz Use…

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Q: Find the gradient of the function at the given point. Function Point (3, 7, 2) f(x, y, z)=√√√√x² +…

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Q: Find the gradient of the function at the given point. Function g(x, y) = ye-* Vg(0,4)= Point (0,4)…

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Q: Find the critical points of the function f(x,y) = x^4 + y^4 - 196xy and use the Second Derivative…

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Q: Find the gradient of the function at the given point. Function Point F(x, y, z) = Vx2 + y² +. (5, 4,…

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Q: Determine the gradient of the curve 3xy + y² = -2 at the point (1, -2)

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Q: Show that a constant function f(x) = b has an average rate of change of 0. Compute the average rate…

A: Average rate of change of constant function fx=b Rewrite;              y=b…

Q: 6. Find the directional derivative of the function f (x, y, z) = x²z – xyz³ + xyz + y – 1 + z from…

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Q: Use implicit differentiation to help you find the value of the gradient for the equation x^2 - e^y =…

A: Given x2-ey=yx-2+8

Q: Find the direction of the maximum rate of increase of f(x,y, z) = y²sinxz² at the point (0,3, –1).…

A: Given the function f(x,y,z)=y2sin(xz2) And the point (0,3,-1)

Q: Find the gradient of the function at the given point. Function g(x, y) = ye-x Vg(0, 9) = Point (0,9)…

A: Given function: g(x,y)=ye-x

Q: The average rate of change of the function f(z) = 13z +4 on the interval [1, 4] is

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Q: f(x,y) = x2-y2 There's a two-dimensional line that goes through the point (5,4) and is parallel to…

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Q: Solve the problem using the CHAIN RULE of differentiation    Imagine a sphere whose radius r…

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Q: Find the gradient of the function at the given point. Function f(x, y) = x² Point (4,4) Vf(4,4) = x²…

A: In this question we have to find the gradient of the function. Note: As per our policy we can solve…

Q: Find the gradient of the function at the given point. Function Point (8,4) f(x, y) Vf(8, 4) = = = x…

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