Average = a] f(z) dz - a. 1. Consider the function f(x) with the graph: 3 2 1 3 4 6.

Q: f is a differentiable function. Then (х) dx ef(x) + C el(x}+C f'(x)ex) + C f'(x) + e(x) + C f(x)ex)…

A: topic - integration

Q: What does it mean for a function of two variables, f (x, y),to be differentiable at a point (a, b)?

A: A function differentiable at a point has a derivative that is defined at that point. This is defined…

Q: For Exercise, refer to the functions f, g, and h defined here. f(x) = -x + 3x 8(x) h(x) = Vx + 2…

A: Given: Formula used:

Q: define y as a differentiable function of x,  find the value of dy / dx at the given point. (x3 - y4)…

A: Given : Define , y as a differentiable function of x . The equation is ( x3 - y4 )6 + ln ( x2 + y )…

Q: For what vaļue of x does the function g(x) =x - 2x? strictly convex? В. x> 0 A. x> 2 D. x -2

A: From the given problem:   gx=13x3-2x2   As we know that:   If f''(x)<0. then function strictly…

Q: E- Find the extrema of the function f:RR, f(x)= +*; +X;X Determine x + x the nature of the extrema…

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Q: A smooth function f : R R has a E R' such that Daf(V f(a)) = 358 Then what is the maximal rate R of…

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Q: Let f(x, y) = xe". What is the maximum rate of change of f at the point (2,0)? O a. 5 O b. 1 O c. 2…

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Q: Determine whether f(x) is differentiable at z = a (Justify your answer using the definition of the…

A: In the question we have to determine the function is differentiable or not.

Q: (c) The tangent plane to the graph of z. = f(x, y) at the point (1, 0, 1) can be described by the…

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Q: dy for the function y = dx 7) Using the first principles definition, determine 2x

A: topic - derivative of a function

Q: Consider the directional derivative of the general function z =, = f(x,y). a) Where is it a i)…

A: The directional derivative of function φ=z-f(x,y) at (a,b,c) in the direction of u…

Q: (e) intersects the graph z = f(x, y) at P and only at P. Given a function f(x,y) and a point P in…

A: State whether the following statements are true or false. Given a function fx, y at a point P in the…

Q: H.W Is f (x) = x. |x| differentiable function? %3D

A: To find  f(x)=x|x| is differentiable function or not.

Q: which then reduces to the function f (x, y) = 1. Suppose that the changes in power x and drag y are…

A: We are given a bivariate function f(x,y) and we have to describe the effect as x is increased and y…

Q: f(x, y) = x² – y²

A: f(x,y) = x2 - y2 Let us firstly find the first order partial derivatives of the given function.…

Q: For function f(x, y) = 5- | 2 E find the maximum value of the directional derivative at (3, 2).

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Q: Let f'(z) = tangent line to the graph of the function h(z) = g(13x+3) at e and g(x) = f(/#). Let L…

A: Given, f'x = ex2  gx = fx L is the slope of the tangent line to the graph of function hx = g13x+3 at…

Q: (ii) Find the length of the curve y = E* from x = 0 to x = 2. %3D

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Q: Evaluate dy and Ay for the function below at the indicated values. y= f(x)= 44 1-- x- 2, dx Ax = -…

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Q: The volume of a right circular cylinder with radius r and height h is V = πr2h. Is the volume an…

A: Given: Volume of a  right circular cylinder =  πr2h  To determine: Is the volume an increasing or…

Q: Using the plane tangent to the graph of the function f(x, y) = ln(y - 2x), determine the approximate…

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Q: The tangent lines which was drawn at points A and B on the following y = f(x) function graph are…

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Q: Find the absolute maximum for the function f(x) = re, x E [-1,3] %3D

A: Given :       function  f(x) = 12x2e-x       Interval  x∈ [-1, 3]    To find : Absolute maximum…

Q: consider the function f(x, y) = esin(= Find the maximum rate of decrease of f at the point

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Q: 22. Let f(æ,y) = xe¥. What is the maximum rate of change of f at the point (2,0)? O a. V5 O b. 5 О…

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Q: Let = (x – 3)(x – 1)2 for a differentiable function f which is defined on the interval [0,4]. %3D dx

A: TO FIND THE CRITICAL POINTS, INTERVALS OF INCREASE AND DECREASE VALUE OF 'X' AT WHICH LOCAL EXTREMA…

Q: ind the local extrema of the function f(x,y)=e* (x² – 2y²) x-y

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Q: Suppose f(r) is a differentiable function. State the formula that determines the length of f(x) for…

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Q: Find the direction in which the function is increasing most rapidly at the point P 0. f(x, y, z) =…

A: Function is increasing rapidly in the direction gradient f at p0

Q: Sketch the graph of y = v4-x², - 2<x<2. a

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Q: Find the linear approximation of the function f(x) = V4 - x at a = 0. L(x) = Use L(x) to approximate…

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Q: For the functions below, what is the direction of fastest increase at  (1, 1, 1)? (a) f(x,y,z) =…

A: The direction of fastest increase for a function at a point is the direction of the gradient of that…

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

A: Given function and the point are

Q: | f(x)dx < Suppose that f(x) < g(x) on [a, b]. By the Comparison Theorem, Is it also true that f'(x)…

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Q: Find the linear approximation of the function f(x) = V1 – x at a = 0. L(x) = Use L(x) to approximate…

A: Given: f(x)=1-x

Q: Match the function with its graph. (x, y) = 1+ x +y p Kx, V) = (x² – y²)* %3D f(x, v) = sin(Ix| +…

A: Answer is mentioned below

Q: Use FunCtion 9(x) = - f (X)tZ gra ph Of Y = fLX) to g raph Y=F(x) 2十 -4

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Q: Give an example of a linear function f(x)= mx + b, with m,b ±0 and an interval a<xsc where f(x)dx=0…

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Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) = 1 a = 3 L(x) :…

A: The solution are next step

Q: The function 5· x. y g(x, y) -20 · y + 2· x + 6 is continuous everywhere on R? except on a line I in…

A: The given function is: g(x,y)=5xy-20y+2x+6...(1)

Q: (c) Find the equation of the tangent plane to the graph of f(x, y) at (1,1,3).

A: Suppose surface S defined by a differentiable function  z=fx,y and point Px0,y0,z0 lie on the…

Q: Determine the value of m such that the function x- y - 5 E + 5 VI - Vỹ f(x, y) = is continuous at…

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Q: The cost, in thousands of dollars, of airing X 30-second television C(x)=40+ 3,000x + 0.064x² Your…

A: Introduction: The second derivative test is a method for determining the absolute maximum and lowest…

Q: Consider the function z = f(x,y). If fx(a,b) and fy (a, b) both exist, and they are equal, then the…

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Q: e of the function g(x y, z) = 1/xz + e%.

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Q: 3. Find the value of c such that the line y = x + 3 is tangent to the curve y = cvx. C =

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Q: Find the point on the curve f (x) = Vx that is closest to the point (2,0). Put your answer in the…

A: Use distance formula and differentiate and put zero

Q: Find the function f(x,y,z) with a magnitude y.

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.