Find the values of x, y and z that correspond to the critical point of the function: f(x, y) 5x² + 1x + 2y + 5y² Enter your answer as a number (like 5, -3, 2.2) or as a calculation (like 5/3, 2^3, 5+4). x= y= Z= =

Q: equation (e^x sin y + tan y)dx + [e^x cos y + x sec^2 (y)]dy = 0 when y(2) = π/6 ? Round off your…

A: Given differential equation is (ex siny +tany ) dx+(ex cosy +xsec2y) dy=0   ; y(2)=π/6

Q: (c) [(317+(31 sint)7) dt (d) ((e)i+e' cos(re)7) dt

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Q: Find y" if y = ax³ + bx+c. (a, b, c constant) Answer:

A: To differentiate the given function

Q: KW. Solve the following 3....2 X... DX. + Xdy - where you... ************

A: By using exact diffential equation

Q: Q2. By finding an apporppriate integrating factor, solve (3x²y + 2xy + y³) dx + (x² + y²)dy = 0.

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Q: Find a function f such that  ∇f = 7e7x cos(3y)i − 3e7x sin(3y)j + z3k.   f(x, y, z) =

A: we need to find out the function f whose gradient is given.

Q: A. 8-24x C. Find the second В. 8х + 10-6х-4 8+ 24x−1 8+24x-5 D c. Y = 4x² + 10x + -5 Find derivative…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: An open-top box is to be made from a square piece of cardboard that measures 18 inches by 18 inches…

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Q: y = √x² (2x - x²)

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Q: 7π Find the area of the sector of a circle of radius 8 units subtended by an angle of 6 nearest…

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Q: 2. (x2) y = y+2(x2)

A: Topic = Differential equation

Q: radius=100mm radius=100mm

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Q: What is the derivitaive of the function? f(x)= log2(xex)

A: We have to find derivative of given function.

Q: Let f(x)= 2 sqrt(-x) +4 Find domain of f

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Q: Determine whether the Rolle's Theorem applies to the function on the given closed interval. If so,…

A: Given functons:- Gx=-2x24x+8 gx=x-323 kx=3x2+30x+3

Q: Directions: Circle each function that is an example of exponential decay (there are exactly five of…

A: As per the instruction, we will be answering the first three subparts. For (a), Graph: For (b),…

Q: If f(x) = f'(x) = f'(1) = = tan a - sec x 4

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Q: Fill in the spots in the integration process below based on the indefinite integral 4x²-25 S using…

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Q: Sketch the plane curve represented by the vector-valued function and give the orientation of the…

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Q: The function f(x) = x²e¹⁰x is increasing on the interval and is decreasing on the interval The…

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation r(t) =…

A: To determine the domain of the given function

Q: 1) Aşağıdaki fonksiyonların Maclaurin Serisini bulunuz. a) f(x) = ln(x) b) f(x) = ln(x+1)

A: See the answer below

Q: Let f(x) = f'(x) = - - 9 cos x + 4 tan x ƒ'( - 7) = =

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Q: Find the point on the line 4x+3y−4=0 which is closest to the point (2,−3)

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Q: Find a point c satisfying the conclusion of the MVT for the following function and interval: f(x) =…

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Q: g(x)=0.3x-1+2 Find the vertical and horizontal asymptotes, if any.

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Q: Find the limit algebraically. lim h→0 f(1 +h)-f(1) h where f(x) = -9x² + 4x - 4

A: To evaluate the limit.

Q: Find an equation of a plane through the point C-5, 4₁-32 Which is or thogonal to the line X= 5+-1₁…

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Q: 20. Let g(x) = x³. a) Find the linearization L(x) of g at a = 4. b) Use the linearization to…

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Q: HE W. Solve the following.. 3..... 2 X). X + Xdy - where you.....

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Q: h(x, y) = In In (1/2¹)

A: Find below the given  elaborated solution

Q: 8

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Q: Function g is a transformation of the parent function f(x) = x². The graph of g is a translation…

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Q: Evaluate the double integral is the region in the first quadrant enclosed by the circle x² + y² = 36…

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Q: 14. Which of the following is an approximate equation of the line tangent to the graph of f(x) = x²…

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Q: 3. Evaluate the following integral S sin x - cos x - dx sin x + cos x O a. In[sinx + cosx| + C O b.…

A: Let's evaluate the given integral.

Q: By changing to polar coordinates, evaluate the integral where D is the disk x² + y² ≤ 25. Answer =…

A: Given data÷ ∫∫Dx2+y23/2dxdy Where D is the disk x2+y2≤25   Now main part of conversion from…

Q: Set up, but do not evaluate, an integral for the length of the curve. ST 2 x = 4 sin(y), Osys (C dy

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Q: 4. Solve the given integral |(2* − xe*")xdx 2 a. 2x² C. In 2 3ex³ + C 4x² +3ex³ In 2 + C 2x² 2 ln 2…

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Q: Find an equation of the plane with point P (2, -1, 3) and containing the line L: x-3 y+4 z-5 -6 10 =…

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Q: f(x) -5 0 Let F (x) be the anti-derivative of f (x) such that F (6) = 15. Then F (0) is O-1 0 1 0 10…

A: Given query is to find the value of F(0).

Q: Find the symmetric equations of the line that passes through points P (-2, 1, -3) and Q (-1,-4, 3).

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Q: 4y³ (x²+4) dy + 4xy+ = (x² + 4) ² dx

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Q: 149. 10/1/2 = -0,693 SEN

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Q: Find the divergence of the vector field F. F(x, y) = 5x + 3y²

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Q: Find the maximum and minimum values of the function f(x, y) = x²y subject to 4x² + 2y² = 24 Please…

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Q: Find the general solution of the differential equation xdy + (x^2- 2y)dx = 0. O y + (1/2)x^2= c O y…

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Q: Find the equation of this particular 5th degree polynomial that goes through the point (-1, 72). -…

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Q: 5 The gain of an amplifier is found to be G= 20 log (10V out) The tasks are to find equations for:…

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Q: The position of a particle moving along a coordinate axis is given by s(t) = t³ - 9t² + 24t + 4, t ≥…

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