[x² - y² If f(x,y)=2x-2y m if y = x if y=x then:

Q: If f(x, y) = x cos y, then fry(0, 1) = ? Select one: O 1 -1 O None of them sin y

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Q: 1. Find the domain of the vector function r(t) =

A: 1. Given Vector Function,rt = lnt+2, t1-t2, 2tt2 -4

Q: (2x²-10a+15) da Integrate: f gở ba tô 2x+3 ln()+ +C n(²²³)+c +C 3 In O2a +3 ln()+ ○ 3 ln() + C o +C

A: We have to integrate ∫2x2-10x+15x2-5x+6 dx.

Q: Find an explicit formula for the general term an of the sequence. {1,- -/-/- 3 5

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Q: (z In z + 5)dz

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Q: x-1 lim x+2+ x - 2 does not exist O +∞ 01 O -∞

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Q: The integral 2 fossin drde is equal to π/2 O-1/2 O 1/2 0 1 00 10

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Q: Given the functions f(x, y) = 4 cos(4x - 6y) and g(x, y) = -6 cos(4x - 6y). af The partial…

A: Here we have to use the concept of partial derivatives

Q: 4. Graph the equation: f(x) = -3, 4, 1/² x + 1²/₁ x<-2 -2 ≤ x ≤ 1 1 < x≤ 4 -3 - 5+ 4+ 1 + 3+ 2+ 1…

A: f(x) = -3 , x &lt; - 2 x -3 -5 -7 f(x) -3 -3 -3 f(x) = 4 , -2 ≤ x ≤ 1 x -2 0 1 f(x) 4 4…

Q: x² 2 =dx 2 √4+x²

A: solution:-∫x24+x2dx=4∫x2441+x24dx=2∫x221+x22dxwe know thatcosh2t-sinh2t=1cosh2t=1+sinh2tusint…

Q: The area of the region enclosed by the two curves y=x²-4 and y = x - 4 is given by

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Q: For the limit, lim (x,y)→(0,0) sin(x² - y²) x² - y² if we approach along y-axis, we will get 1.…

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Q: π/4 [sin (√x) dx 0

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Q: 11. Determine whether the given quadratic function has a maximum value or a minimum value, and then…

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Q: z = (x + y)², x = s²t, y = st². Use the Chain rule to find dz ds for t= 1 and s = 2.

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Q: Evaluate: cot¹ (+) -do None of the choices Ocot³ (1)-cot ()- tan³ () - tan() - ○ cot³ (1)- - tan() -…

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Q: a) b) exist f(x, y) = x²yesy 8x²+7y² Find the domain of the function f. Show that lim f(x, y) does…

A: According to question,Given Function,fx, y = x2 y e5y8x4 + 7y2

Q: If p = (7, 2), then find -2p.

A: If p=7, 2, then to find -2p.

Q: 3. (y + ²+ ) dx + (x + xy²)dy = 0 3 2

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Q: 4. fx(2x - 1)'dx

A: This is a problem related to integration. Please find the general procedure given below. As per the…

Q: = 2√/16 - x² - y2, then the domain of D = {(x, y) x² + y² ≤ 16}. 2

A: We have to choose the correct option from the given options according to the given information

Q: Apply Newton's Method to f(x) and initial guess xo to calculate x₁, x2, x3. f(x) = x² - 13, xo = 4…

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Q: a, b, and I are differentiable functions of the same variable what is the derivative of H ac b +…

A: To find the derivative of acb, here a,b and c are differentiable function of same variable. Let a,b…

Q: 4 Use the substitution z +9=u² to evaluate √√+9

A: Note: Since, the student has asked to solve only question no. 4, so we are solving accordingly…

Q: In(t³ r(t) = 4 lu(t²+1); - (4e-2 - 5e"); _ sin³t 5e²t)j -k, + 1 t3 then the limit lim r(t) equals…

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Q: a) Find the integral / r(t)dt. b) Find parametric equations for the tangent line to the given curve…

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Q: 4. If z = x + iy = (x, y) then the Re(iz) A. Imz B.-Rez C. -Imz D. Rez E. none of the above

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Q: The area bounded by the x-axis, y = x², and y = 2 - x.

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Q: Given the matrices A = - -4 0 4 [ 5 B. If my not possible possible -2 -2 - and B -2 0 189 0 3 3 2 A.…

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Q: 2. Solve the following 4th order linear differential equations using undetermined coefficients: y…

A: We need to solve D.E.

Q: (5x¹2xy)dx + (6y+kx²)dy = 0

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Q: Let f(x, y) = 2x² + 2y² - 4y + 9. Then the level curve f(x, y) = 3 is a: Circle with center (1, 0)…

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Q: Evaluate cosh² x dx }(sinh2n +2) + 0 +x + C O2e²x +4z + C 8 O None of the choices cosh(z)sinh(2)++C

A: We can solve this as follows:

Q: Let u = (4,-1,-1) and v= (2,-2, 2x + 1) be two vectors in space. Find alle ER such that u and v are…

A: The given vectors are u=4,x-1,-1 and v=2,-2,2x+1

Q: Find 7 sin² (7x) dx

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Q: 5. If z = x + iy = (x, y) then the Im(iz) is A. Imz B.-Rez C. -Imz D. Rez E. none of the above

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Q: Given A = -1 0 22]₁ compute 3A

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Q: √x +3 If f(x, y) = xy +7 the domain of f(x, y). Select one: True O False then the point (1, −7) is…

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Q: The domain of the following function: is: f(x, y) = Select one: O A. D= {(x,y) y ≤7-3x} O B. D= {(x,…

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Q: A y=1 x=y² B y=x² C (1, 1) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1,…

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Q: If y = x?, then dy = a Ο 2 Δε Ο 2 Δy Ο 2 Δε Ο π*Δy

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Q: The partial derivative of the function f(x, y) = 4x² – 3xy + 5y-e³+8y with respect to x is: Select…

A: To find out the partial derivative of the equation.

Q: Let z = (y - 2x) ³, where x = s′ s²t and y = st². Use the Chain Rule to dz find when s = 2 and t =…

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Q: If then fyx (1,0) = ? Select one: 0 - sin y -2 None of them 2 f(x, y) = 2x cos y,

A: The required partial derivative is evaluated below.

Q: Find the limit lim 3-0 Select one: 04/3 None of these Does not exist -8/6 00 8x² + 7x-9 6x²-2 if it…

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Q: 5. Find the area bounded by the polar curve r = 4cos30.

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Q: If f(x, y) = 9x² - 6y³ - 7 cos(-6xy + 플) then Select one: O True O False fy(л,0) = -42

A: Given function is f(x,y)=9x2-6y3-7cos-6xy+π2. We have to find fy(π,0) that is partial derivative of…

Q: r(t) = (−2√√ť² – 4, 3 sin (4t), 3 ln (−5 – 2t)), then the domain of r is given by the interval…

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Q: Determine any planes that are parallel or identical. (Select all that apply.) OP₁: -60x + 90y + 120z…

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Q: lim x-x6-x O +∞ 00 ∞- O O 3 1 2 ||

A: topic - limits