4. Sketch the graph of the relation R= {(x, y)| x² – 2x – 2 < y < 2x – x² +

Q: Let k(x) = 1 -x4, where j(x) = y + k(x) and y = x6 - x2. Describe the graph of j(x) based on the…

A: Given: k(x)=1-x4 where, j(x)=y+ k(x) y=x6-x2 Then j(x)=x6-x2+1-x4j(x)=x6-x4-x2+1 The zeroes of the…

Q: The relation f = {(x, y) E R X R Ə is 1. Not function 2. Function 3. On to function 4. One to one…

A: Given :  f(x) = x/x+1

Q: • prove that y` = = for y= (of (1+x)) 1+x²

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Q: The f(x) 6x2 -5x-4 2x2 +x is discontinuous %3D at x = -1/2. By redefine = w , then f will be…

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Q: The graph of f(x,y)=+1-39xy has х у O One saddle point only. O One local maximum point and one local…

A: fx,y=1x+1y-39xy

Q: 1. Find and sketch the domain of f(x, y) = (x – 3y)t.

A: For the solution of the problem follow the next step.

Q: f(x) = (x +2)²(x – 1) f'(x) = 3x(x+2) f"(x) = 6x +6 %3D

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Q: 1) Determine whether the graph has any absolute extreme values on (a, b). 2) Explain the results in…

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Q: 0 <x<1 x + 2 1< x < 3 (x² – 4 1- x (2) Find all the points of discontinuity of the function S(x) =…

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Q: 1. Let f : R3 → R, ƒ(x) = x² + x² + 2ž + 2x2 %3D (a) Draw the graph of the level set So = {r € R³ :…

A: The function fx=x12+x22+x32+2x2 is a function of three variables and we have to draw the graph for…

Q: The graph of f(x,y)=+ 1 +76xy has One saddle point only. O One local minimum point and one saddle…

A: For the given equation

Q: (1-x Find all the points of discontinuity of the function S(x) = } x+ 2 (x² – 4 0 <x<1 1<x< 3 x2 3 |

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Q: Find and sketch the domain of z = f(x, y) = In(9 - x - y²).

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Q: 4. R= {(x,y) x + y ≤ 8} reflexive irreflexive symmetric asymmetric anti- symmetric 1. 2. 3. 4. Which…

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Q: If x + 1 f(x) then find the global minimum of f on the interval [1, c∞)

A: The maxima and minima of a function, known collectively as extrema, are the largest and smallest…

Q: Let f, g:R R defined by if x 1 (x2 and g(x) = 3x + 2. %3D Find f-1 and g-1.

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Q: 1 find all points lif any) of hxizantal and vertical paints of to the curve tangency X={^_f +2…

A: Given that: x=t2-t+2,   y=t3-3t To calculate dx/dt, ddtx=ddtt2-t+2=ddtt2-ddtt+ddt2=2t-1+0dxdt=2t-1…

Q: Describe the domain of the function f(x, y) = In(4 – z – y). O {x.y):y<-x+4}

A: Given: fx,y=ln4-x-y Objective of the given problem is to find the domain of the given function. The…

Q: Graph the firnction (x). Label all the koy points. f (x)= x3 + 3x2 - 4x -12

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Q: Find and sketch the domain of f(r, y) In(r - y) 6. -

A: Given:      f(x,y)=lnx-y9-x2-y2·x2+y2-4    Interval notation : -3,0∪0,3   Set builder notation:…

Q: Let f(x) = x -[r] and f :[1,5) →[0,1). What is the discontinuously type of f(x) at the point x = 3?

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Q: 9. Use the given graph of f (x) x2 to find a number 8 such that %3D if |x – 1| < 8 then |x2 – 1| <;…

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Q: 14. Determine the constraints a and b such that f(x) is continuous for all values of x. ax - b x ≤ 1…

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Q: Describe the end behavior of the graph. 20 16 12 +12 +16- 20 O Ax)→ -co as x→-o and (x)→ -co as x→…

A: To determine the end behavior of the below graph.

Q: Find and sketch the domain of the function f(x,y)= exy/ x-y2

A: See the attachment

Q: Find the linearization L(x) at x= a. f(x) = 2x° + 5x - 3 a= 3 L(x) =

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Q: The graph of f(x,y)=++13xy has X y -13ху O One local maximum point only. O One local maximum point…

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Q: Determine the minimum for the relation y (x + 16)(x - 8). -64 -16 -226 -144

A: To determine- minimum  for the given relation.

Q: Let f (x, y) = 4-y² In(y–z²) %3D Draw a picture of the domain of this function.

A: x,y ∈R2

Q: Find the Domain (b) g(x) = In(x² –- x) %3D

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Q: Write the domain of the relation y = arccsc x. x≤-1 or x≥1 -1≤x≤1 0≤x≤1

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Q: Let f(x) = 4x – 8a2 + 5x. Find the absolute maximum and the absolute minimum of f on [0, 2].

A: To find  The absolute maximum and absolute minimum of f(x) at [0, 2]

Q: Find the linearization L(x) at x = a. f(x) = - 4x3 - 3x+1 a = - 3 L(x) =

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Q: Describe the end behavior of the graph. 20 16 12 4 3-3 12 16- 20 f(x)→-co as x→-co and f(x)→-co as…

A: Consider the graph

Q: 1. Sketch graphs of these three quadratic relations on the same set of axes. 1 a) y = -3x² b) y = x²…

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Q: 2. Let f(x) = eª + 4e* 1 for x E [0, 3]. Determine the length of the graph of f.

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Q: 6. Given (*) = vx , sketch the graphs from = y = -2f(3x +3) - 4 Label at least 2 points on the…

A: f(x)=xf(3x+3) =3x+3f(3x+3)=3 x+1y=-2 f(3x+3) -4y=-23 x+1 -4

Q: Which values of C makes r(x) (a) left-continuous, (b) right-continuous (c) continuous x2 +3 for x 2

A: If the function r(x) is left-continuous, then use limx→-1-rx=limx→-1+rx, to determine the value of…

Q: ) The domain of the function y = In(1 – x²) is R – [-1,1].

A: Log (x) is defined for every  x is positive real number .

Q: 1. Find the absolute minimum and maximum values taken by the func- tion f(x, y) = x² + y² – x – y +1…

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Q: Let f(x) = Va and g(x) = x² – 1. Find go f and determine its domain. |3D %3D

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Q: The domain of the finction f(x, y) = In(-x² - +1) is:

A: The domain of a function is the range of the values that can be input into the function. The…

Q: 2. If f(2) = e*, describe the images under f(2) of horizontal and vertical lines, i.e. what are the…

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Q: Discuss the continuity in R3 of the function f(x, y, z) %3D x2+ y2+z2 -1

A: Given: f(x,y,z)=1x2+y2+z2-1.

Q: Letf (x) = 4x +9x - 12x 4 5. %3! Find the absolute minimum value of f on the interval [0, 3].

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Q: 7. Find the minimum of, f(x1, x2) = 2xỉ - x1x2 + 2x3 + x3 – 2x1x3 And check the second order…

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Q: The domain of the relation A is the set of all real numbers. Ay if |x-y| ≤ 2

A: Given relation is A=(x,y): x-y≤2, x,y∈ℝ Here x is the domain of the relation.

Q: Form the PDE by eliminating the arbitrary functions from the relation z = f(xy)

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Q: 5. Find the domain of the function: y = In () x-4

A: y=lnx-1x-4