f(1, 1) = f₁(1)f₂(1) f(1, 2) # f₁(1)f₂(2) for x = 1, y = 1,2 then x and y are: dependent O independent O

Q: d x4. dx x³J3.a x*J3.b0 X' x³J3c0 x*J4 d O

A: We first write the general form of j_n then we take the derivative of x^4j_4 with respect to x and…

Q: b) Find and classify all the critical points of f(x, y) = 3x²y + y3 – 3x2 - 3y2 +5. %3D

A: The solution is given as

Q: x?y x² + y² Define the function f: R² → R by ƒ(x, y) = if (x, y) # (0,0) if (x, y) = (0,0) (a) Let e…

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Q: The antiderivative of the function f(#) + 8* is -8 + 2.0a2 +e 4 +4.0a2 +c -4 + 16.0a? + c -4 4.0a2 +…

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Q: Find the S(x* +) dx xe-1 А. 1x? + c e-1 4e xe+1 В. Ix2 + c e+1 2e xe+1 С. 1x3 + c e-1 Зе xe+1 1 D.…

A: Given query is to find the derivative of the expression.

Q: f(1, 1) = f₁(1)f₂(1) f(1, 2) # f₁(1)f₂ (2) for x = 1, y = 1,2 then x and y are: dependent O…

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Q: (x, y, Z) = è + xlny + ylnx find fz fx fxx fy 5) fxy Fyx

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Q: Evaluate * Vx² – 1 dx.

A: Given,  ∫ x2-1x2dx

Q: (18) Find [S], where S = {(a, b, c)|a, b, c E [100], a <b, a <c}.

A: Here is how the set S is defined: S = {(a, b, c) | a, b, c ∈ [100], a &lt; b, a &lt; c}   We must…

Q: Determine fr and fy from f(x, y) = x³ + x²y + xy² + y³ ○ fx = x + xy, fy = x + 2xy ○ fx = x² + xy,…

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Q: If xly then gcd(x,y) = y. إختر واحدا:

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Q: 3. Given fxx(x,y)= 4x² On Support 0 Otherwise Let U=Y-X. Determine f(u) (Including the Support of U)…

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Q: Determine if f(x, y) is continuous at (0,0) where x²y² √x² + y² 0 f(x, y) =. if (x,y) = (0,0) if (x,…

A: To determine whether  is continuous at where

Q: az + b If T(z) cz + d a, b, c, d e R. Show that T(RU{∞}) = RU {∞} if and only if exist

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Q: Find the absolute maximum and minimum values of f on the set D. f(x, y) = x4 + y4 − 4xy + 6, D =…

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Q: Decide whether or not the real function In (eon 2) I+0, = (1) 1= 0, is continuous at r = 0.

A: The given function is fx=ln cos2x2x2     if  x≠0-1                if  x=0. Compute the limit…

Q: 2 (2² – 337) (2? + g²)³ iv) fay(æ, y) = v) fyv (x, y)

A:

Q: 1 x+R+ 2)²(x+ x+ R+ 4) dx (Hint: Let u= x+R+2 x+R+4

A: ∫1x+R+22x+R+42dx

Q: Q2 Let f(x) = c x= 0,1,2,3, . 1-find c ? 2-find EX(X – 1) ?

A: Given a probability mass function; f(x)=c2xx!, x=0, 1, 2, 3, ... 1. We know that a very important…

Q: 1. Let f(x, y): x-y x+y+1 Find:

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Q: dy Let y = x?Vx2 + 1 then is dx x (3x2 + 2) Vx2 + 1 x² +1 A (3x2 + 2) Væ2 +1 B x² + 1 2x2 (3x2 + 2)…

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Q: O Determine if f(x, y) is continuous at (0, 0) where x² y ² f(x, y)=√x² + y² 0 if (x, y) = (0,0) if…

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Q: Find the values of af /ax and af lay at the point (4, 5) if f(x,y)=x² + 3xy + y -1

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Q: 46) Evaluate V(3r + 1)dx 2(3r+1)7 O s(3z+1) 2 O 2(3z+1)7 +c 3 O D(3r+1)1 + c 2

A: We have to solve the given integration

Q: when that this 1x² + y² Shothathis sho (x, y) (0,0) and f(0,0) function is continous at (0,0)

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Q: Locate and identify the critical points of f(x, y) = (x²-1)²-(x²y-x-1)²

A: The given function is fx,y=-x2-12-x2y-x-12.   The critical points can be found by solving the system…

Q: Cov(x,y)=v(y) if x=y True False оо

A: Given problem Given that   Cov( x,y ) = v( y ) if x = y Ans) True First Option

Q: Let f(x, y) be a function such that F(s, t) = f(s- 2t, t2) f-(2, 1) = 5, fr(0, 1) = 3 fy(2, 1) = -1,…

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Q: 2 2 ex: f(x, y, z) = x² - by ² fx (x, y, z) = fy(x, y, z) = fz(x, y, z) = 2 ezete

A: f(x, y, z) = (x2 - 6y2)/(y2 + 2z2)    =&gt; fx(x, y, z) = ∂/∂x [(x2 - 6y2)/(y2 + 2z2)]…

Q: f., f, and f_, and evaluate each at the given point. x'y ху f(x, у, 2) 3- (4, 1, –1) x + y + z fx(X,…

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Q: (a) f(2, 1, 2) (b) f(-3, 2, 1) (c) f(0, 0, 0) (e) f(t, 1², –t) (d) f(a, a, a) (f) f(a +b, a – b, b).…

A: Given: The function f(x,y,z)=xy2z3+3 where f is a function of x, y, and z. To find: f(2,1,2),…

Q: If W= x³y?zª +2xy +z Then w¿(- 1,1,2)= -31 .4

A: Proceed as shown below...

Q: The critical points of the function f (x, y) = 1 – x² + 6x – y + 8y2 are - O a) (3,0) and (-3,0) O…

A: