2- Show that the function U(x,y)= 3x²y-y² + y is Harmonic and then find it's Harmonic conjugate V(x, y)

Q: Find the exact value, if any, of the following composite function. Do not use a calculator. 3x tan…

A: Using fact that arctan(tan(x))=x

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 6 cos(t)i…

A:

Q: 7. Use the Divergence Test to determine whether thee following series diverge or state that the test…

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Q: Find the indicated derivative and simplify. -[9x log x6] dx [9x log x] = 9x1 dx

A:

Q: It is estimated that t years from now the population of a city will be P(t) = 20(60 + 3)² - 1100t.…

A: The population of the city after t years from now is given by, P(t) = 20(60+3t)2 - 1100t

Q: Express as a single logarithm and, if possible, simplify. log (x²-2x-35) - log (x²-25) log…

A: Using log(a)- log(b)= log(a/b)

Q: A person's height depends on their age. (a) This situation describes a function, y = f(x), where the…

A:

Q: What is the domain for the exponential function f(x) = -5log(x-2)? OD: (xe R) OD: (xe R|x>-2) OD:…

A: Here we have to find the domain of the given function.

Q: Write the negation for the following statement: If Juan is Rosa's father, then Miguel is her uncle…

A: Explanation of the answer is as follows

Q: (a) Use sigma notation to write the Maclaurin series for cosлx. (b) Use sigma notation to write the…

A: Write  Taylor series first then try to rearrange

Q: 13. Evaluate the triple integral: In y (z) dzdydx y2

A: Given :∫12∫1x∫y2lnyz dz dy dx=I

Q: Find g'(x) if g(x) = 6xex g'(x) =

A:

Q: 2. Use reduction formula to evaluate the integral: fsins x dx.

A: Reduction formula

Q: INTEGRATE dx ¹.Sa 4x1 2.fdx

A: According to question,Given Integral,1. ∫dx4x-1

Q: In triangle ABC, let M be the midpoint of AB and N be the midpoint of AC. Suppose that you measure…

A: Concept: Midpoint theorem of the triangle: According to the midpoint theorem, "the line segment in a…

Q: sto

A:

Q: Find the cross products uxv and vxu for the the vectors u = 3i-j-2k and v=i+2j-3k.

A:

Q: A parabola is formed when a plane slices through a cone. Which of the following describes the…

A: This question is based on Conic sections.

Q: Find the values of x y (x+y²) (2+i)= 5(x+y;)

A:

Q: and the local maxima, local minima, and saddle points of the function, f(x, y) = x³ + 3xy + y³

A: Topic = Derivative

Q: 5. A tank is full of water. Find the work required to pump the water out of the spout. Water weighs…

A: A tank is full of water. Find the work required to pump the water out of the spout. Water weigh is…

Q: Determine the domain and range of the function. 2+ 1 1-3 1-2

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Q: First use appropriate properties of logarithms to rewrite f(x), and then find f'(x). f(x) = 2 In…

A:

Q: Let f(x) = 4x + 4 and g(x) = 2x² + 2x. After simplifying, (fog)(x): =

A: To find the value of composition of given two functions.

Q: дz (B)If Z = f(x, y), x = s² - t², y = 2st. Prove that s მა 2 (s² + t²) of af əx I t дz at II

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Q: Find dy if y=t² & t = √h and h = x² dx

A: Given :y=t2t=hh=x2

Q: 8. Use the Integral Test to determine whether k4 Σk5 +55 k=1 converges.

A: Solve the following

Q: Q5 Answer by "True" or "False" of the following questions: (four only) [6 1- If I[ A=[§__25], then…

A: Topic = Integration

Q: 13T Use reference angles to evaluate sec Enter the exact answers. For the number , either choose…

A:

Q: Use partial fraction decomposition technique to evaluate the integral: x² S dx. (x+1)3

A:

Q: 1. Find the derivative of f(x). 3x³ 2x²-x-5 - (a) f(x) = √x (b) f(x) =

A:

Q: S²₁₂ So 1-y² √x² + y² √x²+y² xyzdzdxdy

A: We know that integration power rule is - Integration of xn is xn+1/n+1 +C . Here C is integral…

Q: 2. A cheetah chase a deer which is 100 m ahead. The time in which the deer takes 10 leaps the…

A: We want to find number of leaps in which cheetah catch up the deer.

Q: A. d²y dx² B. d²y dx² 4 + 7y=0 dy dx - 4y = 8e²x - 12

A:

Q: Evaluate the function & (x) = x+8 for the given values of x. Write exact answers in simplified form.…

A: Given that, k(x) = √(x+8) Find values, k(-8), k(7), k(8), k(-10), k(6).

Q: dy 2) x - 2y = x³ cos4x

A:

Q: Can you please write out an explination that shows steps?

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Q: The graph below is the function f(x) 4 -5 -4 -3 -2 -1 1 2 Determine which one of the following rules…

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Q: дz (B)If Z = f(x,y) , x = s² - t² , y = 2st . Prove that s дл 2 (s² + t²) of дх дz ||

A: Use total derivative and chain rule

Q: f(x) = e-* cos(2x) dx

A:

Q: What is the area of the largest rectangle that has its base on the x-axis, its lower left corner at…

A: To find the area of the largest rectangle with given corner points.

Q: The flight path of a rocket, launched from the ground, is modeled by y = 0.25(40x-x²), where y is…

A: The problem is solved below

Q: If tant -4, what is tan (t = π)? Enter the exact answer. tan (t) =

A: Given tant=49To find tan(t-π):

Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, 0, 0),…

A: Given points  P ( 0, 0, 0) and  Q ( 1, 9, 3)

Q: Find y'. x³y² = x² + y²

A:

Q: The plot below represents the function f(x) 8 7 6 5+ 4 3 1 2 3 4 5 2 1 -5 -4 -3 -2 -1 -1 -2+ Solve…

A: Given the graph of function f(x) is

Q: A parabola is modeled with the equation x² - 12x + 4y + 24 = 0. Which is the domain and range of the…

A: This question is based on Parabolic function domain and range.

Q: c) real numbers 2. Show that the decimals below are rational. a) 0.4 b) 0. 21 c) 0. 14

A: As per the company guidelines We can first three parts of  question . Please understand. Kindly…

Q: Find all vertical asymptote(s) for f(x) = r answers using limits. = √√7-√√3-x |x +41 (x2)) ●

A:

Q: Use the given information to find the unknown value. y varies inversely with the cube of r. When -…

A: y varies inversely with the cube of x. When x=5 then y=1.