x³ - y³ z = f(x, y) = x² + xy + y² 0 for for (x, y) = (0,0) (x, y) = (0,0)

Q: -i+3j and Y = 4i - 2j + 2k. -Y. 3. Consider the vectors X and Y in R³ where X Find the unit vector…

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Q: On which interval or intervals or if there is any, the Mean Value Theorem applies for f(x)=√x² - 4…

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Q: When is a function Fan antiderivative function f? of a if F(x) is continuous for all x in the domain…

A: Given , When function  F(x) is called an antiderivative of a function of f(x).

Q: Q1. Calculate the area of the region lies inside the diagram (r= 4 cos 20) and outside the circle (r…

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Q: Evaluate: lim, 0 sin 2t t³ (t-1)²

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Q: 29. Given dx where a>0, at what value of p will the integral become convergent? c. p = 1 a. p> 1 b.…

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Q: 12. DETAILS ZILLDIFFEQMODAP11 1.R.001. Fill in the blank. The symbol C₁ represents a constant. d =…

A: The solution is given below.

Q: Given a function y² z f(w, x, y, z) = 2(w + 1)²x - xe² + W which of the following is not part of the…

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Q: f(x) = 2²3 on (0, ∞) x+3

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Q: 0, -5<z<0 92, 0≤z<1 then 11, 1<x<5 E If f is the Fourier series of g(x) = f(z)- What does f(-5)…

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Q: Instruction: Evaluate the following Integrals. Write your COMPLETE solutions neatly and organized.…

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Q: dx (x²+1)(x²-4)² dx (x²+4x+4) (x²-4) dx x(x+1)(x²+5x+6) S S S

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Q: Give a general solution of the differential equation y"+4y=-3 sin 2t.

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Q: 24 The following limit gives the derivative of a function f(a) at a point zo: √8th-2 lim h 0 h

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Q: Solve for fazy for f(x, y, z) = 4x³y²z - e²zy¹ + + 4y - x¹6

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Q: What is the equation of the tangent line to the curve y = x^ + 2x? −x+8 +2x2 where x = 1? y = 7x - 3…

A: Let's find equation of tangent line.

Q: x sin æ+tan² I lim, 0 1-cos

A: We can solve this as follows:

Q: (i) Find the linear approximation of the function f(x, y) = 1 - xy cos πy at (1, 1) and use it to…

A: Here, the given function is: f(x,y)=1-xycos πy To find the linear approximation of the function. For…

Q: Find the integral. [col³ (x) csc ³¹ (x) dx (Use symbolic notation and fractions where needed. Use C…

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Q: Given the piecewise function f(x) = = Why is f not differentiable at x = 0? f is discontinuous at x…

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Q: Question 4b. Determine the average value of f f(x) = b) The method of integration is: evē+3 over the…

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Q: Given: f(x, y) = arctan Find: F ƒ(x, y) dxdy x² - y² (x² + y²)² 3²-x² (x² + y²)² -y³ (y³ + xy²)² y²…

A: Given: fx, y=arctanxyTo Find: ∂2fx, y∂x∂y

Q: 口 38 Which one of the following equations describes the tangent plane to the curve, f(x, y) =…

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Q: 2. 2y² SS dxdy 1 y

A: Disclaimer: Since you asked multiple question,we will solve the second question for you. if you want…

Q: Given a function, Based on the function, S-3 F(s) = 2 S² +6s+13 a) Determine ƒ(t). b) Based on…

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Q: What is the derivative of y = sin (x³ – 3x)?

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Q: Find the integrating factor by inspection then solve the following differential equation. Show your…

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Q: . Calculate the area of the region lies inside the diagram (r = 4 cos 20) and outsid the circle (r =…

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Q: Given w = xex + ln(x²yz3) Determine дш дх O дш дх δω дх ди дх дш дх = ex(1 - x) + = xẻ +1+ 11 N|X 2…

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Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. Find the unit vector…

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Q: For the function f(x) given below, where x > 0, evaluate lim f(x). X18 f(x) = ln(9x³ + 10) - In(2x²…

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Q: Which one of the following is the domain D for f(x, y) = ln (2²-(y-2)²) ? Select one alternative:…

A: The given function: fx,y=lnx2-y-22.We need to find the domain.

Q: Which of the following represents the symbol for the indefinite integral? S dx dy b a Σ

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Q: Evaluate the given limit. Show your complete solution. limx→∞ [e5z + x²]

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Q: Let f denote a piece-wise defined function whose graph on the closed interval [-3, 3] is sho below:…

A: Here, the function is continuous on: (-3,-1)∪(-1,3)

Q: Find y' 1. 3x − y + (3x-y)5 = 100

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Q: 8. 1 (1+x)√√x / dx

A: We have to find out integral

Q: find  the area of the  region bounded by the  curves y²=4px and x²=4py

A: To find the area.

Q: What is the derivative 7 of y = (3x + 1)²? 21 dx dy = 6 (3x + 1)²¹ dx = dy 6 (3x + 1)² dx = 7 (3x +…

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Q: Evaluate the line integral F. dr where F(x, y, z) = x²y i+ x³ j+e² tan-¹ z k and C is the curve of…

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Q: 3 s) Suppose that the direct demand and direct supply functions are q = - - 1 and q = 1 respectively…

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Q: 1. S w²dw √2w-w²

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Q: Evaluate: limt o sin 3t t5 (t-1)² using L'Hôpital's

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Evaluate the surface integral [[ F.ds where F(x, y, z) = (x³ +y³) i+(y³+z³) j+(z³+x³) k S and S is…

A: We will calculate surface integral , use of divergence theorem

Q: Question 13 Given: ez + xy = 1 dz Find: dr zey te O dz 8x 8x dz 8x Za zerx Ty IZ ce¹² ze Ty

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Q: 50° 60° 70° ?

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Q: Solve the following initial value problem using Laplace transform d'y dy dt -2y = 6e³t; dt² y (0) =…

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Q: Determine a root of f(x) = 2* +3 cos(x²)-2 with 10-3 accuracy.

A: Given :f(x)=2x+3cosx2-2

Q: X3-4X Which of the following graphs represents the function 1(x)=2x²+2x-4 -? 5 1 2 f(x) O O 4 7

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Q: What is the derivative of y = √/x? 1x² X 2 2 1 X X 2 23

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