Verify Green’s theorem in the plane for R C (3x 2 − 8y 2 ) dx + (4y − 6xy) dy, where C is the boundary of the region y = √ x and y = x 2

Q: Let y = 3x². Find the change in y, Ay when x = 3 and Ax = 0.3 Find the differential dy when x = 3…

A: The given function y=3x2 We have to find ∆y and dy.

Q: Find the extreme values of the function and where they occur. None O Minimum value is at x = e¹/4;…

A: To find the extrem values of the following function and to determine where they occur.y=lnxx4

Q: dz Given z = xy + sin(xy2), with x(t) = 2t + 1 and y(t) = -t², find dt t=1

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Q: ton = 15/8 where Toz Ø180 Find cos20

A: Please see the below picture for detailed solution.

Q: 2 كل ك 0.5 , 3- = (f(x رشد -

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Q: 33-41 Use logarithmic differentiation to find the derivative of the function. 33. y = (2x + 1)³(x² −…

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

Q: Consider the following. e¹ - 4x = 3 (a) Find the exact solution of the exponential equation in terms…

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Q: m to be removed -

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Q: 3. (b) Identify the curve by transforming the given polar equation to rectangular equations. r = 6 3…

A: (b) The polar equation is given as , r=63cosθ+2sinθ          .....1 Identify the curve by…

Q: Determine if each of the following vector fields is the gradient of a function f(x, y). If so, find…

A: WE can determine if each of the following vector field is the gradient of a function f(x,y) .

Q: xx (x)dx X 3TT 28

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Q: (4) Determine if the alternating series converges ∞ Σ(-1)" sin t . n n=2

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Q: options Yart 1. Find Sin(t) part 2. find cos (t) 10 10 options 8 ㅋ 능 None 10 ㅋ 10 8 3. 10 4.…

A: Topic- unit circle WE are given a point on the unit circle as -810,-610we know that on unit circlex…

Q: Evaluate f(x) = 3 sin x + 5 cos at x = π/3. 1. f(π/3) = 4 4√3 2. f(π/3) 3. f(π/3) 3√3 4. f(π/3) =…

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Q: (5) Determine if the alternating series converges Σ(-1)^n. 8 n=2

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Q: Without evaluating integral, prove that 1 dx S 0 /2+x-x² 2 < 1 √2

A: Prove that , 23≤∫01dx2+x-x2≤12

Q: Determine whether the integral is convergent or divergent. 100 (x - 6)³ 8 S² O convergent O…

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Q: Find a parabola with equation y = ax² + bx + c that has slope 10 at x = 1, slope -14 at x = -1, and…

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Q: J.J. Sm 35.) a. cos 210° 36.) a. cos TC 6 DICUS DIJ b. cos 90° b. sin TU 3 C. COS SEU c. sin(-120°)…

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Q: 4. TT/6 t sin

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Q: 4. A parabola has focus F( 11, 8) and directrix x= -17. Find its standard equation

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Q: 26. tan ³0 sec ³0 de

A: Topic = Integration

Q: 3₂ If t=15157, evalvate if possible Part 1. Sin t 13 له b) none - 이글 e) 9 + ا (a C) - 0) ) 6)-1 یہ -…

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Q: Calculate the gradient of f(x, y) = xy at (x, y) = ( − 1, - 2). Vf(-1, -2)

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Q: Find the equation of the line tangent to the graph of f at the indicated value of x.  f(x)= 17e^x…

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Q: Is the integral -- 1 XT dx convergent or divergent?

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Q: 8. Find the slope of the tangent line to the parametric curve x = 4 cos(t), y = 3 sin(t) when t=…

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Q: Approximate the area under the curve graphed below from x = 2 to x = 5 using a Right Endpoint…

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Q: 39. y = (cos x)*

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Q: 2. The position of a rider on a Ferris wheel is an example of periodic motion. Find three other…

A: 1 )A Rocking Chair

Q: Consider the following. 4x/15 = 0.3 (a) Find the exact solution of the exponential equation in terms…

A: find solution

Q: Show that the function f(t)=√t+√√1+t-4 has exactly one zero in Solve the equation √t+√√1+t-4 = 0 to…

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Q: -2 + ax 27. lim (√x² + X-8 - 29. lim (x² + 2x²) 8118 √x² + bx unil 3

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Q: Sketch the graph of the function and determine whether it has any absolute extreme value on its…

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Q: nd the value of f(e¹0). e¹⁰) e¹0) =_

A: We have to find the value of f(e^10)

Q: Suppose that f(x, y, z) = x²yz - xyz³ is a function of three variables. 1. Find the gradient of f(x,…

A: The given function is; f(x,y,z)=x2yz-xyz3.

Q: (c) x³ - y³ lim (x,y)→(1,1) X-y

A: C) lim(x,y)-(1,1) (x3-y3)/(x-y) D) lim(x,y)-(0,0) (x-y-x6)/(sqrt(x-y)-x3).

Q: Please show your answer to 4 decimal places. Find the direction in which the maximum rate of change…

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Q: Convert the general form to standard form of parabola

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Q: Find the intervals on which the graph of f is concave​ upward, the intervals on which the graph of f…

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Q: 5/136 A cable weighing 25 newtons per meter of length is suspended from point A and passes over the…

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Q: x) = (x-10) ¹

A: Given query is to find the critical points.

Q: Use a calculator to solve the following equation for on the interval (0, π). cot (0) =1/2

A: cot(θ)=12tan(θ)=1cot(θ)=2tan(θ)=2θ=tan-12θ=63.4349

Q: Find an equation of the tangent line to the curve y=x√x that is parallel to the line y = 3 + 3x. y =

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Q: SHOW COMPLETE SOLUTION Find the points of intersection between the circle (x-2)²+(y-6)² = 40 and…

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Q: "roblem 9. True or False. Explain your choice carefully. is convergent. nv2, n = 1, 2, 3, ... is…

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Q: Consider the following. 62 1 + ex (a) Find the exact solution of the exponential equation in terms…

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Q: Give the standard equation of the circle satisfying the given conditions a.) Center 1,5 diameter 8…

A: Note: As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: 1. (a) (b) (c) (d) Find Maclaurin series for the function e-2x 2² 2³ 1+2x-x + _ 2! 22 2x+x 3! 1-2x²…

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Q: lim X ड Hy गं

A: We have to find limit