Let a be a constant and f(x, y) = x³ – 3axy + y³. Determine that the following - statements are "True" or "False".

Q: Let c>0 be a constant.  Is this result true or false?

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Q: Find constants c1 and c2 such that F(x) = c1xex + c2ex is an antiderivative of f (x) = xex .

A: Given: Fx=c1xex+c2ex is an antiderivative of fx=xex To Find: c1=? and c2=?

Q: Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously f(x, y) = x2 − xy…

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Q: Find ∇2f, given that f(x, y, z) = 1 / (x2 + y2 + z2)1/2.

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Q: Determine whether the functions f1(r) = e2*, f2(x) = e-2" , and f3(x) = sinh 2x are linearly…

A: To determine whether the functions f1x=e2x, f2x=e-2x, and f3x=sinh 2x are linearly independent on…

Q: Determine the linear approximation of f(x) = x' at x = 1. а. у3 9х +8 O b. Not in the list О с. у--…

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Q: Let f(z) - 4z-1 pnd alz) - ar+b, where a pnd b are positive constants. If the composite

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Q: Determine the linear approximation of f(x) = x at x = 1. O a. Not in the list О b. у3 3х +2 с. у %3…

A: A detailed solution is given below.

Q: Q1. Find the linearization of f(x, y)= x² – xy + 12y? +3 at the point (3, 2).

A:

Q: Suppose that f(z, y) = 10z²y² + 8z? + 2y? then find the discriminant of f.

A: We have to find the discriminant of the function of two variables fx, y. It is given that the…

Q: Determine the linear approximation of f(x) = x² at x = 1. a. y= 2x +1 O b. y = 2x - 1 O c. y=- 2 x-1…

A: Given: f(x)=x2, x=1 To find: Linear approximation at given point.

Q: Given f(x, y, z) = x³yz². Find f.(1,1,1).

A: The equation we have , f(x,y,z) = x3yz2 We have to find out fz, Now we differentiate f(x,y,z) with…

Q: Show that if f (x, y, z) = 0 then = -1.

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Q: Given the function: f(x,y, z) = x°y2² + æy° +y°z Find а. fazy: (x, y, z) b. fazyz(1, –1, 1) -

A: Given the function :  f(x,y,z) = x3y5z7 + xy2 + y3z

Q: Where a is a constant, then a is equal to:

A: Since, the joint probability distribution function is given .. Here, wa want to the value of 'a'

Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

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Q: Find f, and f, for f(x, y) = 12(6x-3y +8)°. %3D 1,(x.y) = %3D

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Q: Find f, and f,. f(x, y) = 13x In xy

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Q: Differentiate g(N) = rN g'(N)= with respect to N. Assume that K and r are positive constants.

A: We need to find g'(N).

Q: Show that f(x) = 2a + 3b is continuous, where a and b are constants

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Q: Let A > 0 be a fixed but unspecified constant, and let f(x) = xn= (In x)", x > 1. Compute f'(x).

A: our objective is to find the derivative

Q: af axdy of f (x, y) = xy(x+y — 1) — x² Find-

A: The given function is: fx,y=xyx+y-1+x2   As we know that; The Power Law: ddxxn=nxn-1 The Product…

Q: Determine the linear approximation of f(x) = at z = 1. O a. y= 9x +8 O b. y=- 9 x-8 O c.y = 9x - 8 O…

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Q: Find the interval in which the function is positive. f(x) = x2 - 7x + 10 %3D I. (- , 2) II. (2, 5)…

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Q: Eliminate the arbitrary constants a. x = -In t, y = at + bt?

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Q: Find x' for x(t) defined implicitly by x+t°x+t -8=0 and then evaluate x' at the point (-2,2).

A: x3+t3x+t4-8=0Differentiate w.r.t…

Q: Find x' for x(t) defined implicitly by x +tx+t° - 5=0 and then evaluate x' at the point (- 1, - 3).

A: Follow the procedure given below.

Q: Find f, and f, for f(x,y)=y In (2x+7y).

A: F(x,y) = y ln(2x + 7y) To find : fx and fy

Q: a.) If     f(x) dx   = 4x9 − 8x6 + C, find f(x). f(x) =

A: Given: ∫fxdx=4x9-8x6+c                                          ..1 for finding fx, we differentiate…

Q: Let f(x) = 2 – x². Over the interval [0, 2], calculate (a) R4 and (b) L4

A: As per the instruction, we will be answering only the first question. For (1), For L4:

Q: (c) Show that |(−1,1)| = |R|, where (−1, 1) = {x € R : −1 < x < 1}.

A:

Q: Show that u(x,t)= f((x+a*t)+f(x-a*t))/2

A: Given PDE is utt=a2uxx subject to ux,0=fxutx,0=0 We know that the general solution of the PDE is…

Q: 16. Determine if 4x – 3xy + yʻ is homogeneous or not. If it is homogeneous, state the degree of the…

A: Given : f(x,y)=4x2-3xy+y2   To Check : f(x,y) is homogenous or not and it's degree, if it is…

Q: problem in photo attached

A: The given function is,

Q: Let f(x, y) = x² + xy + y² where x = 3(t + s) and y = e2st, find . as

A: we have given f(x, y) where x and y are function of s and t.  We have to find the partial derivative…

Q: Find f,, fy, and f, for f(x,y,z)= 5xy+ 3xz + yz.

A: It is partial derivative

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: If f(x) = Rsin TCX +S,f' 12 and 2R ,then the constants R %3D 2 0. and S are respectively. 1

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Q: Given f(x, y) = x® + 3xy4 – 2y°, find f-(x, y) = fy(x, y) =

A: If f(x, y) is a function then, fx(x, y)  is differentiation of f with respect to x making y variable…

Q: For f(x, y), find all values of x and y such that f,(x, y)= 0 and f,(x.y)= simultaneously.

A: Please refer to the image below

Q: Find the minimum and maximum values of f(x,v) = x2 - 3y + y³, x² +4y? < 36

A: Given,         f(x,y)=x2-3y+y3  and   x2+4y2≤36.

Q: Let R=[0,1]x[0,1]. xy3 dA= R.

A: Let's find.

Q: Let f (x) = n², then / f (x) dx = + C where C is an arbitrary constant. True False

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: Given f (x,y) = 3 – 2x² – 2xy – 2y² – 16x, find and classify all critical points of f. -

A: Calculate fx, fy , fxx , fyy , fxy for f(x,y)=3-2x2-2xy-2y2-16x as follows.…

Q: 2R then the constants R TCX If f(x) Rsin .2 S,f' and f(x)dx and S are respectively.

A: Introduction :Here we have asked to find the value of R and S

Q: Let a +b = 4, where a 0 for all x, prove that g(x) dr + g(x) dx increases as (b- a) increases.

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Q: b) Let X₁, X₂, Xn-f(x) = {0x-(0*) x>1 e. w. find Suff. Comp. St.

A: Given that

Q: The function f(x) = x³ – 3x² + 5 is concave upward on the interval O (-∞, 1) (1, co) (-∞0, ∞0) O…

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