What is the general Chain Rule? What form does it take for functionsof two independent variables? Three independent variables?Functions defined on surfaces? How do you diagram these different forms? Give examples. What pattern enables one to remember all the different forms?

Q: The figure shows the graphs of four functions. One is the position function of a car,one is the…

A: The figure of four functions is given.

Q: FUNCTION of x?

A: To be a function  Each value of x (set A) have single image in y (set B) Or the function should pass…

Q: differentiable and

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Q: analytic function

A: We have to find out the analytic function. It is given that v=tan-1(y/x)             ......(1)

Q: relation

A: Domain of f  =  {29, 4, 8, 20}  =  X. For the element '4' in set X, there two images '-2' and '0' in…

Q: (a) Find the linearization of f () = at a = 4. x+1 Enter the linearization using the equation…

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Q: In Section 1.6, we will learn additional techniques to graph functions by recognizing…

A: "Since, you have asked a question with multiple subparts, we will solve the first three for you. If…

Q: What do you mean by generating function?

A: In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by…

Q: The graph is a translation of one of the basic functions y= x, y=x, y = Vx, y= x]. Find the equation…

A: The given graph is

Q: Describe the First Principle method and the Power Rule method for finding the derivative. Which…

A: In first principle method the slope of the curve is used as a derivative This is called the first…

Q: Explain in a sentence what the partial derivative of f with respect to x represents in the context…

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Q: Give an example to explore numerically how a function behaves near a particular point at which we…

A: Solution: Consider y = f(x) = 1/x is the function Since at x = 0, this function is going to be…

Q: How do I differentiate this function using the chain rule: f(x)=[x^2/sin(x)]^6

A: Given,           The function is fx=x2sinx6.

Q: How do you test a twice-differentiable function to determine where its graph is concave up or…

A: According to the Second Derivative Test for Concavity, Consider y=fx be a twice-differentiable…

Q: Sketch a picture of the graph, plotting a minimum of five points. Then describe any transformations…

A: Given query is to plot  the graph and describe the transformation.

Q: Find the relative extrema of the function g(x) = x sech x. Use a graphing utility to confirm your…

A:

Q: differentiate y= (4x + 3)2 using the Chain Rule. a. What is the outer function? b. What is the…

A: Given: y=4x+32

Q: Find a function f that has the derivative f′(x) and whose graph passes through the given point.…

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Q: Find the point on the line y = x that is closest to the point (5, 7). [Hint: Express the distance d…

A: NOTE: Refresh your page if you can't see any equations. . the given line is  so any point on the…

Q: The sand in an hour glass drops at a constant rate of 2.5 cubic millimeters every second. The amount…

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Q: function

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Q: Find a function f that has the derivative f′(x) and whose graph passes through the given point.…

A: It is given that the derivative of the function f'x=4.

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: The chain rule is used to differentiate a function which is the multiplication of two functions. Let…

Q: y = 2x – 5 on interval ( - 0, 0)

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Q: When is a function described in pieces?Give an example?

A: A function is said to be piecewise if it is defined using more than one formula where each formula…

Q: A right triangle has one vertex on the graph of y=x3,x >0 at another at the origin,and the third…

A: The right triangle which has one vertex on the graph of y=x3,x >0 and another at the origin,and…

Q: Discuss

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Q: Zez analytical function or not?

A: We check whether w=zez is analytic function or not.

Q: Find a function f that has the derivative f′(x) and whose graph passes through the given point.…

A: Given: f'(x)=2x  At (1,0)

Q: 11. Communicate Precisely Describe two different representations that show a relation that is also a…

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Q: How to distinguish an Even function from an Odd function and the relationship between them.

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Q: Draw simple graphs of the first and second derivatives of the function y = f(x) whose graph is given…

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Q: A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point…

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Q: The position of a car driving along a straight road at time tt in minutes is given by the function…

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Q: A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point…

A: Given points are x,0 lies in x-axis,2,3 and 0,y lies in y-axisSlope between 2,3 & x,0 = 3-02-x =…

Q: Identify the graphs of the nonlinear functions. Select all that apply.

A: Given: The graphs of the functions To identify: The graphs of non - linear functions.

Q: Using the graphical technique, evaluate the residues of the function

A: The function f(x) has three poles on the complex s-plane. Hence we have to find three different…

Q: 2. During typhoon Ambo, PAGASA tracks the amount of accumulating rainfall. For the first three hours…

A: During typhoon Ambo, PAGASA tracks the amount of accumulating rainfall. For the first three hours of…

Q: The function f is linear. Can f be an odd function? Explain how you know

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Q: Sketch the graph of the function ? = x3-6x2+12. Using the ff. First derivatives (critical…

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Q: QUICK CHECK 4 What is the analog of the Two-Path Test for functions of a single variable?

A: The two path for a function of single variable is f(x) is if f(x) approaches to 'a' as x approaches…

Q: Identify the point of diminishing returns for the input-output function. R is the revenue and x is…

A: The given revenue function is R(x)=-12x3-4x-7  where 0≤x≤2 We know that the point of diminishing…

Q: (1 point) Match the function with one of the graphs below. A B.

A: the graph of function is given below.

Q: When is it possible to compose one function with another? Give examples of compositions and their…

A: A new function can be created by combining the two pre-exist functions. This new function can be…

Q: function with form y = ax

A: Given,  A power function y=axp passes through the points 3,781 and 6,71296. The equation of power…

Q: Range: 4f)--(* + 1) - 2 Parent Function: Transformation: Domain: Range:

A: First simplify the given function then here parent function is x^2. So draw the graph of x^2. And…

Q: A closed box with a square base is to be constructed. The top and sides will be made of material…

A:

Q: Explain the effects of changes in “a” and “c” on the graph of y = ax2 + c. Transformations –…

A: When the graph of two functions are identical but translated, mirrored or compressed by any constant…

Q: A right triangle has one vertex on the graph of y = x3, x > 0, at (x, y) another at the origin, and…

A: Given, A right triangle has one vertex on the graph of y = x3, x > 0, At (x, y) another at the…