4rabc 1 is Given that the sum a + b+ c is 3 The volume of an ellipsoid a2 62 fixed, show that the ellipsoid of maximum volume is a sphere. c2

Q: 1 log3(r – y)*

A: Given; fx,y=1log3x-y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

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Q: : Find the area of the region R enclosed by the lines y= x, y x/3 and y = 2?

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Q: Find the area of the region bounded by the graphs of f(x) = x^2 − 4x + 3 and g(x) = −x^2 + 2x + 3.…

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Q: Let R=[0,1]x[0,1]. хуз dA= 41x2+1 R

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Q: ind the point/s of intersection of each of the following figures given below, draw the element and…

A: Area

Q: 161 n + e 20 n 2n + tan (103 n). CO The sequence is n=1 O divergent as its limit is o 161 O…

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Q: Let D be solid cone /x² +y² <:<1. Use CYLINDRICAL COORDINATES and find the mass if the density is ô…

A: To find the mass .

Q: 1 Evaluate: xInx In Ob. In Oc. -In 6 O d. In 6

A: LetI=∫e-3e-21xlnxdxPut ln(x) =uDifferentiate w.r.t.x1xdx=duI=∫-3-21udu.We know that…

Q: 6 Evaluate the limits lim: X+ co X 6.

A: Topic:-   limits and continuity

Q: The dimension of the vector space P3 is equal to: Select one: O 5 none of the others O 2 4 O 3 ):…

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Q: Work Problem 1 ( Consider the function f(x) = x4 + 2x3. (a) Find the x- and y-intercepts of the…

A: As per guidelines, I can answer only one question and maximum three sub parts of a question. Since…

Q: Learning Task: Determine the volume of the solid that will be generated by revolving the area…

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Q: To find a particular solution for y" - 36y = 44 sin(21) %3D with the method of variation of…

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Q: Graph the following function Function المعادلة الرئيسية у3- cos (x) y=A cos (Bx+C)+D A= y B= C= D%=…

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Q: nP 00 クの In=1 2+n3

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Q: Find the local max and local min and saddle points of F(x,y)= 2x^2+y^4-4xy

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Q: '217-г3—1 limx → 6- Solve x2 – 5x-6

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Q: Find the solution of the following Differential Equations 5) y"-ky' = 0, y(0) = 2, y'(0) = k .

A: We have to find the solution of given differential equation.

Q: Consider f(x, y) = 3a² – 4y² and U = cosn î + sin }r î. %3D %3D Find the directional derivative of f…

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Q: The implicit derivative formula on a surface F (x, y, :) = 0 is: *--() F Evaluate d:/Əx on the…

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Q: For the function: f(x) = 2sin (G) on the interval [0,4Tt], find: Relative max = (t,[ ? ]) Relative…

A: This is a problem related to maximum and minimum of the function. Based on the general formula and…

Q: Show that the function f defined by 1, (x, y) = (1, –1) f(x, y) = x2 + Y (x, y) # (1, –1) x +y is…

A: Here, the given function is: f(x,y)=1;   (x,y)=(1,-1)x2+yx+y; (x,y)≠(1,-1) lim(x,y)→(1,-1)

Q: Which of the following statements is true about the function f(x) = a3 + 6x2? a. None of these. O b.…

A: Solve the following

Q: Consider the function f(x) = x4 + 2x3. (a) Find the x- and y-intercepts of the graph of f (if any).…

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Q: 12x + 30 -dx x²+ 2x – 8 Let In M = What is the value of M? O (x+4)3 +C (x– 2)9 O (x-4)²(x+2)º None…

A: ∫12x+30x2+2x-8dx

Q: sin 4.x if x > 0 Suppose f(x) = {0 if x = 0. Find f'(0) using the definition of derivatives. x+4x if…

A: We have to find f'(0).

Q: Given an acceleration vector, initial velocity (uo,vo), and initial position (Xo.yo), find the…

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Q: 1. Find the approximate area of the region bounded by the curves (x) and g(x) = x* - x. Give + 1…

A: We have to find the area between the given curves.

Q: 11

A: As per policy only first question is answered. Please refer to the image below

Q: Prove that 17 is the only prime number of the form n- 64.|

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Q: 6. The average value of f(x, y) over the rectangle R = {(x, y) | asxSb, csysd) is 1 fave (b- a)(d –…

A: We have given that average value of function is favg=1b-ad-c∫∫Rf(x,y)dA

Q: L(sin² at)

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Q: Which of the following statements is true for the function f whose derivative is f'(x) = (x – 1)e" ?…

A: Given :f'(x)=(x-1)e-x

Q: b)I bounded by y 2 0, z 2 0, x > 4z, and 16 > x + y. Evaluate the following triple integral: Let E…

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Q: Find the minimum and maximum values of the function y = 8/x2 + 1 – 7x on the interval [0, 8] by…

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Q: Sketch the graph of a function f with domain [1, 5] satisfying all the following conditions: •…

A: This question can be solved by the concept of nature of graphs.

Q: Evaluate the function at the given value of the independent variable. Simplify the results. (If an…

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Q: A ball is thrown upward from a height of 1.5 m at an initial speed of 50 m/sec. Acceleration…

A: as per guideline i can only answer one question . answer is in next step

Q: Determine all the relative minimum and maximum values, and saddle points of the function h defined…

A: The given function is  h(x,y)=x3-3x+3xy2

Q: (b) J x– 6)(x+2)²

A: The given integral is: I=∫xx-6x+22dx   We know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: 2n + tan (103 n) ) n=1 161 n + e 20 n 2n + tan (103 n) The sequence is n=1 O divergent as its limit…

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Q: Consider the curve C of equation (x² - y + y?)2 = x² + y? . Among the indicated options, select the…

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Q: 8 x3 dx Vx2 + 36

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Q: A rocket sled having an initial speed of 153 mi/h is slowed by a channel of water. Assume that…

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Q: Find the area between the curves y=|x- 4 and y=-+4 . y=\x=4| 2 O 120 sq. units O 48 sq. units. 64…

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Q: In the standard (x,y) plane, what i the distance between (3, 4) and ( 2)?

A: Topic:- geometry

Q: What is the critical point?

A: The objective of the question is defination of critical point.

Q: Consider and know that the function g defined by 1 g(x, y) = cos (TX /y) + log3(x – y)* Answer the…

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Q: If A = {2,4} and B = {1,4, 5}. Define a binary relation R1 and R2 from A to B as follows: R1 {(a, b)…

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