Find all second-order partial derivatives of the function. f (x,y) =x³+xy³ + y²

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Q: Find the derivative of each function using the definition of derivatives. Use the formula of defini...

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Q: Q Find Haclaurin Sertedf then fuucboors Ć Sinx

A: Here we have to find the Maclaurin series of the given function,  a) f(x)=11-xb) f(x)=exsinx  

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Q: The derivative of a function f(x) at a particular value of x can be approximately calculated by f(x)...

A: The given function is f(x)=7e0.5x.

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Q: 2. Find the maximum and minimum of the function f(x,y) 1 subject to the x² +2y² constraint x* + 2x²y...

A: Solution is given below:

Q: (a) Let f(x) = tanx- 2, g(x) = x5 + x³ and h(x) = Vcsc5x. Then find %3D the f(g(h(x))), using chain ...

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Q: Consider the following integral. | 4x7 V4 + 15 dx With the right substitution, the integral becomes ...

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Q: Find 2- ベ-3 2メ-3 2X+3 X+4

A: Please refer to the image below

Q: The cost C, in dollars, of renting a moving truck for a day is given by the function C(x) = 0.20x + ...

A: Since you have asked a question with multiple parts in a single request, we would be answering only ...

Q: T(E) = N= T'(4) Evoluate (t) NG) for t=L,

A: First we find r'(t) then put t=1

Q: (3 – x if x < 2 if x 22 - 4. f(x) = { is discontinuous on the interval (- 0, 2] %3D -3

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Q: (a) Find the cost and revenue if the company produces 500 units. Does the company make a profit? Wha...

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Q: ) Find the number k>0 such that the region bounded by the curves y = x² and y = kx has area 9 square...

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Q: The cost C, in dollars, of renting a moving truck for a day is given by the function C(x) = 0.20x + ...

A: As per Bartleby guidelines rule I am answering only top 3 questions.

Q: sin x dx 1-2 cos x

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Q: 1. What does the following numerals represent? 51651 五万六百五 Input the numbers in decimal system. Do n...

A: 1. What does the following numeral represent = 50605 The number is =  5 times 10000 plus 6 times 100...

Q: Let f be a function defined by z = f(x,y) = 3xy² – 4y. Find the approximate change in z when x chang...

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Q: Which diagram correctly shows [4|? 4 units 4 units + 01 8 units + -4 4 units 4 units

A: To determine which diagram represents |4|

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Q: V. Discuss the continuity of the following functions. If discontinuous, identify the discontinuity. ...

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Q: (3x² + 1 +)d: x 2x2 (2+v) dx 2. 3. хсos(2x? + 7)dx 4. (7x³ + 4x²)dx 5. V1— сosxdx

A: Integration xn dx=xn+1 /n+1

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Q: z is jointly proportional to the square of x and the square of y. If z=364 when x=6 and y=5, find z ...

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Q: Let a = ci + jand b = 4i + 3j. Find c so that the angle between a and b is Round your answers to fou...

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Q: Question 6 Let Fx) be an antiderivative of fux), with F(O) = 50 and J, f(x) dx = 12. what is F(5) = ...

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Q: oo o o O dy Find using implicit differentiation, for the equation z +y = 11 is , da x4 x4 x4

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Q: consider the following  5^-x/50=9 a) find the exact solution of the exponential equation in terms ...

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Q: 1) An equilateral triangular plate with 6m side is submerged vertically in a tank of water so that i...

A: Here, the top surface of the triangle plate is 2m  below the free surface of the water. Therefore, ...

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Q: Find the integral. In 8x dx

A: I=∫ ln 8xx dxln 8x =t18x(8) dx = dtdxx =dt

Q: Find the indefinite integral using the substitution x = 8 sin 0. (Remember to use absolute values V6...

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Q: 7. Evaluate S(xcos 3x) dx

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Q: Let A = and B = be vectors in R3. Find the unit vector in the direction of the vector A - 2B.

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Q: Graph the continuous function with the following properties. f is even f'(0) and f"(0) are undefined...

A: We have given some conditions:f is evenf'0 and f''0 are undefined but f' is differentiable everywher...

Q: dx (x+2)Vx+1

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Q: Question 15 Without any computation, find the values of sinx dr = Blank 1. Blank 1 Add your answer

A: As sin x is an odd function.

Q: Calculate the distance and midpoint of the line segment joining the each pair of points (a) (0, 1, ...

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Q: If dy/dx= 5y+2 and y(0)= 3. What is the value of x when y=2?

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Q: The curve -4x – 3y³ – 7x + 5y = 2 is shown in the graph below in blue. Use the graph below to draw l...

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Q: Use partial fractions to find the indefinite integral. (Remember to use absolute values where approp...

A: This question is based on indefinite integral using partial fraction.

Q: b. 2 sin? x+3 sin x = -1

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Q: Evaluate the double integral over the rectangular region R S SR 4xy°dA; R = (x, y) : –4 <x < 4, –14 ...

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Q: du/dx dx Let u = Begin by rewriting the integral into the following form. du = dx du x2 + 12x + 1 dx...

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Q: Find the coordinates of the centroid of the solid generated when region bounded by x2 + y? – 6y = 0 ...

A: The given curves are: x2+y2-6y=0 y=6-x

Q: Find the first order partial derivative with respect to y of the function f (x, y) = x³y² + 3æe". 3a...

A: Differentiate given function with respect to y treat x as a constant. 

Q: Write out the form of the partial fraction decomposition. (Do not find the numerical values of the c...

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