Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola y = 4 - x2. (smaller value) (larger value)

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A: slope of tangent line to a curve y = f(x) is given by          m = dydx

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Q: The graph of f is shown. y y = fx) 6. 6. 12 18 24 Evaluate each integral by interpreting it in terms…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: ecot x 20. J sin² x(e- cotx) ax is equal to A. ecot x 1 + C ecot x C. -ecot x + C D. –ecot x + C

A: Given problem:-

Q: -2 e* sin(x) -dx 1+ x2

A: the solution is as follow we will solve the given problem by numerical method  Trapezoidal rule

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Q: y = (x+6)(x+8)® (x+3)³(x+5)5 Differentiate using Logarithmic Differentiation

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Q: Does g(t)=3t^5+10t^4−30t^3+70 have any inflection​ points? If​ so, identify them. An inflection…

A: The given function is: g(t)=3t5+10t4-30t3+70 And, the derivatives are:…

Q: For a general graph of a function a = g(y) that may go to the left and the right of the y-axis, %3D…

A: Follow the procedure given below.

Q: 2. Let f be continuous and differentiable everywhere. Suppose that f(-1) = f(1). Show that there are…

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Q: Evaluate the indefinite integral: (In æ)5 dx +C %3D

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Q: is 8 g/cm while a

A: answer is in next step

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A: The correct answer is option (d).

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Q: Σ (-1)" (2n +1) The Maclaurin series expansion of tan-r is given by tanr = for r € (-1,1) Utilize…

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Q: Evaluate the definite integral. Use a graphing utility to verify your results. 25 dx

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Q: Determine whether Rolle's Theorem applies to the following function on the given interval. If so,…

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Q: lim (e2x – 1)* X→0+ Find the limit using L 'Honital's RI

A: We have to find the limit by using L 'Hopital' Rule Rule

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Q: 10 a. lim 1+3 x - 2 10 b. lim T7 x -2 2x +1 c. lim T-2 x – 3

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: Suppose you deposit $3000 at 4% interest compounded continously. Find the average value of your…

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Q: (y-3)/(x°+1) dy = y dx is a separable differential equation. Select one: O True O False

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Q: Express the given parametric equations of a line using bracket notation and also using i. j. k…

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Q: Vcos² x*(x-1)³ (x+Vx)² 3. y = 2 Differentiate using Logarithmic Differentiation

A: y=cos2x43x-13x+x2

Q: b)Find the average value of f(x) = x3 – 1, 0<x<4

A: We can find the average value of the function as below.

Q: 7. Integrate: S sec? (n²x)dx A. 2n tan n² + C В. x sec2 п2 + С C.금tan(T2x) + C D. x sec nx + C 8.…

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Q: Use vectors to find the lengths of the diagonals of the parallelogra that has i + j and i – 18j as…

A: Given query is to find the length of the diagonal.

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Q: 2- consider the set of all finite subsets of N, is this set countable or not, prove it?

A: Consider the set of all finite subsets of N, is this set countable or not, to prove it.

Q: that you are using. Σ n=1 n/2+1 •a.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Quest An exercise machine with an original price of $970 is on sale at 10% off. a. What is the…

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Q: (x²–2x)° 2. у %3 x2 Differentiate using Logarithmic Differentiation

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Q: Find Duf at P. f(x, y, z) = 6x³yz?; P(2, –2, 2); u =

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Q: Find positive numbers x and y satisfying the equation xy=20 such that the sum 4x+y is as small as…

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Q: Express in sigma notation. (a) a1 = a2 + Az - aq + ag (b) -bo+ b; - b2 + bg - b4 + bg

A: Since, the student has mentioned to solve question number part (a) and part (b), so we are going to…

Q: Find the derivative if the following and simply to its simplest fo a) y= (4t2 – 3t + 2)-2 (x+3)* b)…

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Q: Consider the following integral. Sketch its region of integration in the ry-plane. 110zy da dy (a)…

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Q: 3. If sin a and a is in quadrant I, use the double-angle identities to find sin (2x), cos (2x), 8…

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Q: Consider the following integral. Sketch its region of integration in the xy-plane. dy dz (a) Which…

A: Firstly , find the limit of 'x' and 'y' . i.e, In the given integral , find the limit of  'x' and…

Q: How much energy (in Joules) is required to convert 126 grams of ice at -26 °C to liquid water at 40…

A: Given, Mass(m)= 126 g Temperature of ice(T1)= -26°C Temperature of water(T2)= 40°C The specific heat…