a) Determine the domain and range of the function z = 4 - V9 - (x² + y?).

Q: Ax, y) = In(x +y)

A: In this question, we have to find the domain and range of f(x,y)=lnx+y As we know that the domain of…

Q: Calculate the approximation for the given functionand interval:                    M4, f (x) =√x,…

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Q: Find the mioimum and maximum values of the function subject to the gicen fCx.y)=6x?+Sy? 3X+10y=3

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Q: Find the domain and range of the function.

A: Given : The function f(x, y) = ln(xy - 6)   To find the domain and range of the function.

Q: ): Apply Rolle's theorem for the function f(x) = 9x² – 36x + 27 over the interval [1, 3]. Justify…

A: Given :- Apply Rolle's Theorem for the function fx = 9x2 -36x + 27 over the integral 1,3.

Q: The domain of the function ,y) = In[x* +y² – 1) is:?

A:

Q: he domain of the function f(x) = Vx+5 is In(3-x) %3D

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Q: a) Find the points on the graph of f(x) = 2x- 3r²- 12x + 8 where the tangent is 3. horizontal.

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Q: Find and sketch the domain of f(x, y) = /9-x²-y² Vy²–1 What is the range of f ?

A: Given function is  fx,y=9-x2-y2y2-1 The graph of given function is

Q: Q=- Find the Zero and its oider for the function fiz) = 1- Ki+Z+ ¢ ?

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Q: Find the points of discontinuity of the function f(x)={1−x2,x<0x+2,x≥0 if they exist.

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Q: The function f(x,y) =26-2x²-y² is continuous at point (2, -3). .A True .B False

A: The objective is to determine whether the statement, " The function fx,y=26-2x2-y2 is continuous at…

Q: What is the domain of the function f(x, y) = x² /ỹ – In(x)?

A: topic -  function domain and range

Q: Find f'(2) if y = f(x) is the nonnegative function defined for x, y > 0 by the equation x" = y?.

A: To find f’ (2), if y = f (x).

Q: Find the roots of the function f(x)=(2x-1)(x2+2x-3) with x belong to R

A: f(x)=(2x-1)(x2+2x-3)=0 We have find all the real numbers that make f(x)=0 because it is given that x…

Q: Find the minimum and maximum of the function in the specified interval. 1. f(x) = x² - 6x + 9 on…

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Q: Find the global extrema of the function f(x)=x3−6x2−15x+100 on the interval [−3,6].

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Q: f(x, y) = /4 – x² – y² + V1 – x? -

A: To find the domain of the function, f(x,y)=4-x2-y2+1-x2

Q: Find the extremum points of the function f(x,y) = y² +x*y +x² - 2y and determine the nature of the…

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Q: Use a formula to express y as a function of t if y = 6x + 4x and x = t- 1.

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Q: The slope of the line tangent to the graph of f(x) = 15 – 3a2 at the point z = -8 %3D 48 96 O 12 O…

A: Solution is given below : Answer: 48

Q: Maximise the function f(x, y) = 4xy² subject to r + y? = 2.

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Q: Sketch the domain of the function.  f (x, y) = √(81 − x^2)

A: Sketch the domain of the function.       fx,y=81-x2

Q: (B) The function f(x) = x² + x +1 has no fixed point, prove that.

A: Let X be a nonempty set and f : X → X. A point x ∈ X is a fixed point of  f, if f(x) =x.  If no…

Q: Find the Zero and its oodex for the function flz)=1- Ti+Z+

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

A: Relative extremum of a function are critical points of the function. Critical points of a function…

Q: Find and sketch the domain of f(x, y) = 9-x2-y2 Vy2-1 %3D What is the range of f?

A: We have to find the points where the function is defined.

Q: 2. Find the domain and range of the function y = Vx + 4

A: We Know that  Domain: The set of all points over which a function is defined. Range: The set of…

Q: Find the length of the are of the function x² = 4y from x = -3 to x = 3.

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Q: (2022) , find feua (0) (1-x3 2x given f(x) 2

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Q: Find the domain of the function. Express the exact answer using interval notation. f(x) = To enter…

A: Consider the function  f(x)=25x+8

Q: Locate the absolute extrema of the function on the closed interval. f(x)= x³ 12x, [0, 4] -

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Q: Calculate the approximation for the given function and interval.                         M6, f (x) =…

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Q: Use the Intermediate Value Theorem to show that the graph of f(x) = 4tan(x) – x + 1 intersects the…

A: Please note that according to guidelines only first Q is solved. Please repost the other question.

Q: Determine the stationary values of the function z = x3 – 6x² – 8y² and distinguish between them

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Q: Find the point on the graph of f(x) = Vx that is closest to the point (5, 0). (x, y) =

A: Use distance between point concept and then differentiate

Q: of the function. + 3y + 11

A:

Q: Find the linearization of the function at a . f(x) = sqrt  x    , a = 4

A: Consider the provided function, fx=x,    a=4 Find the linearization of the function at a. Apply the…

Q: Find the slpoe of the secant line between the values x 1 =-1 and x 2 =3 for f(x) = 8x - 3

A: Givenf(x)=8x-3x1=-1  x2=3

Q: Find the point on the graph of f(x) = Vx that is closest to the point (6, 0). (x, y) = %3D

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Q: Find the equation of the function f whoseg 3 f'(x) = (0, 4) %3D -- 1 + e

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Q: Consider the function y= g(I)= -z² + 3c + 6,

A: The derivative of the function f(x) with respect to x is given as .

Q: What is the largest interval in the function f(x) = x² - 2x + 1? A. (-∞, 1) B. (-∞, 0) C. (1, ∞)…

A: Function -  parabolic function    Option A is the correct option.

Q: 2. Sketch the graph of the function (b) ƒ(x, y) = Vx² + y? – 1 -

A: our objective is to draw the graph.

Q: Find the global extrema of the function f(x)=3x4−6x2+2 on the interval [−2,2]

A: Global extrema of a function exists at critical points or at the end points of the interval.…

Q: 2. Sketch the graph of the function (a) f(x, y) = Vr² + y? (b) f(x, y) = Vx² + y? – 1 %3D

A: Given a. fx,y=x2+y2b.fx,y=x2+y2-1

Q: The range of the function y= 16-x2 is the interval [0, 0)

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Q: (b) Use the result of part (a) to find the direction in which the function f(x, y) = x³y - x²y4…

A: Given:

Q: Consider the function f(x, y) = 4x² – 8y² subject to the condition x + y = 25.

A: