The domain and range of f(x,y)=81-x^2-y^2

Q: Can a function have an inflection point at a critical point? Explain

A: Show that: Can a function have an inflection point at a critical point?

Q: Differentiate using implicit differentiation 3 2 4.3 r-2/0 =0 +04 03 +-04 2 3

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Q: Determine the maximum value of the function f(x)=2sinxcosx on the interval [0, π]

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Q: Suppose a cut is made through a solid object perpendicular to the x-axis at a particular point x.…

A: Given that a cut is made through a solid object perpendicular to the x-axis at a particular point x.

Q: Sketch the x^2 And the derivative And integration

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Q: What are the two graphical interpretations of the Midpoint Rule?

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Q: derivative of f(x)= 1/(x^2+5) is

A: Given,          fx=1x2+5

Q: Apply the second derivative test to find all relative extrema. - 5)² (a) f(x)=(x

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Q: Find the absolute extrema of the function on the closed interval. f(x) = 7 – x, - [-4, 4] minimum…

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Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

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Q: How is derivatives utilized in solving for the dimensions and total area of a box?

A: Here we to write how is derivatives utilized in solving for the dimensions and total area of a box.

Q: Describe the Chain Rule for the composition of two differentiable functions in your own words.

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Q: at the point (2, –1). Find the maximum rate of change of f(x,y): x2 + Y

A: For maximum rate of change we need to calculate magnitude of gradient bat point (2,-1)

Q: find the derivative of f(x) = (x²+4)(3x³ - 2x) at the point x = - 3[ use product rule] %3D B.

A: We have to find the derivative

Q: Find the area of a triangle bounded by the yy axis, the line f(x)=4−67xf(x)=4-67x, and the line…

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Q: Differentiate f (x) = (ex + e-x)/(ex - e-x)

A: We have to differentiate the function: fx=ex+e-xex-e-x Here two function are in ratio so we need to…

Q: Differentiate the function. 3. %3D In(x)

A: Given y=3ln(x)differeniatey'=ddx3lnxy'=3ddx1lnxApply exponent rule:  1a=a-1y'=3ddxln-1xApply chain…

Q: Find the area of a triangle bounded by the yy axis, the line f(x)=7−67xf(x)=7-67x, and the line…

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Q: Describe the domain of : POINT 2) f(x, y) = Ln(2 + x + y) %3D

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Q: 1 F(x) = -1. tanh 3x

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Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – the…

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Q: Explain the difference between the Discrete and Continuous Variables.

A: Discrete Variables are the variables whose values are obtained by counting since these variables…

Q: (8 points) Find the slope of the line tangent to the graph of 1 f (x) = 2x* – 32x + 17x2 – 9x + 4 at…

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Q: Find the absolute extrema of the function on the closed interval.

A: Given,  The function is  y=3-t-3 Interval is [-1,5] The given function is a modulus function which…

Q: 7. Differentiate the function using quotient rule. хех y = x + ex

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Q: Find the area of a triangle bounded by the yy axis, the line f(x)=3−16xf(x)=3-16x, and the line…

A: GIVEN DATA: Triangle is bounded by the equation of line fx=3-16x                         line…

Q: F(x) = -7+ x2 INTERUAL-ピ-3 -2. AUERAGE RATE of

A: Given query is to find the rate of change for the given interval.

Q: Differentiate the function. f(x) = (3x2 − 4x)ex f '(x) =

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Q: Use Intermediate Value Theorem to show that the equation

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Q: Differentiate the function. y = etan(8) y' =

A: The given function is y=etanθ.

Q: Explain the rule of maximum and minimum using Derivatives with an example?

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Q: Find the area of a triangle bounded by the yy axis, the line f(x)=7−13xf(x)=7-13x, and the line…

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Q: Show two ways to differentiate ƒ(x) =

A: The function f(x)=1x10. We have to differentiate this function.

Q: Describe how to use the second derivative test to find relative maximum and minimum values of a…

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Q: f(x) = ln (1/x^6)

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Q: Explain graphically: The endpoint approximations are less accurate when f , (x) is large.

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Q: Differentiate the function y = (x + 8) In (x +8). y' = %3D

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Q: How to find stationary points for f(x) = x^2-6x^2+9x and their local max or local min

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Q: Find the value k that makes the function continuous. kx f (x) = x > 9 - -7x – 7, x < 9

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Q: Sketch level curve of f(x,y)=x2-y2

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Q: Find the domain of the function. 4) f(x) = x2 + 3 A) (-«, -3) u (-3, ∞) C) (-3, «) 4) B) (-*, «) D)…

A: We will find out the required domain.

Q: Find the point on the line y = – 4x + 2 closest to the point (8, 9). - The function giving the…

A: Given, equation of line : y = -4x +2 And  The point : (8, 9) {outside the line}

Q: 2. Is the function given by F(x) = x². 5x + 6 continuous over the interval (-5, 5)? Why or why not?

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Q: Vx + y + 1 f(x, y) ,æ In (y² – x) х — 1 -

A: Given: fx,y=x+y+1x-1,xlny2-x A function f(x,y)=Mx,y,Nx,y is said to be continuous on the points…

Q: A gutter is to be made from a piece of sheet metal that is a inches wide by bending up pieces of…

A: Width of the metal sheet = a inches We bend up x inchs on both sides.  So width of the gutter is =…

Q: Describe how you would use the second derivative to determine a local minimum or maximum.

A: Given data is: How you would use the second derivative to determine a local minimum or maximum

Q: Can the Mean Value Theorem be applied to the function f(x) = 1/x2 on the interval [−2, 1]? Explain

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Q: y 1-

A: The solution is given below in the next step:

Q: the shaded area shown in the figure is bounded by the line with equation y = 12-7x-x² and the line…

A: given functions are                                              y=12-7x-x2, y=4…

Q: Estimate the slope of the tangent to the function f(x) = (x + 1)^2(x - 4) at the point of abscissa…

A: Introduction: A tangent line is one that intersects a curve at the so-called point of tangency.…