C. Evaluads the Sum 20 [ (₁²+3) ² (

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Q: 3. Waile si Sigma Notatimi 1. 12-201 4 곱 so times 나스

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A: Using inverse operator

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A: Giveny=2cosec(1-3x)Aim: dydx

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A: Given curve, y=4-x2 Portion of given graph rotate around X axis in first quadrant, Therefore Put x=0…

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A:

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A: We have to find width and height of rectangle.

Q: a) e b) e-t Q24) The Integrating factor which make (3x2y + 2xy + y³)dx + (x² + y²)dy = 0 exact, 15.…

A: A detailed solution is given below.

Q: √4x²(x³-5) dx = x³ (x¹2 - 25x² + 250x6 - 1250x³ +6250) + c O 16(x³ - 5)4 + c O(³-5)5+c O (2³-5) 5+ c

A: See the details solution in below

Q: O Determine if the line and plane intersect. If so, state the solution. T: -2x+6y + 4z_4=0 L: [x, y,…

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Q: Solve the following equations 2)3x+2 = 27 1) 2Ln(√x + 3) + 2Ln(√x-1)=Ln(6x-7) I 1 1

A: Let's solve both equation.

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Q: Solve the following Differential Equations with Laplace Transforms y" - 6y + 15y = 2 sin (3t), y (0)…

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A: Given :  A piece of cardboard measuring 14 inches by 9 inches is formed into anopen-top box by…

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A: The objective is to find the equation of tangent line .

Q: 10. The y" of y = (2x¹ + 4x³)(3x¹ − x³) is - a. 336x6 +420x5-120x¹ C. b. 336x5 +420x4-120x d. 48x7…

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Q: Use - -1-1(x Let f(x) = 9x +7 In (x+1), x>-1. Find - dx (Simplify your answer.) x=0 to find the…

A: By using ddxf-1x=1f'f-1x to find the derivative of the inverse at the indicated point. Let fx=9x+7…

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Q: 31. The function fƒ: R→ R is defined by f(x) = (a) Show that f is a bijection. (b) Determine f¹(x) x…

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Q: Six 2 CSC ² 2x - x cos 2x) dx

A: We know, ∫cosmx dx= sinmx/m  ∫sinmx dx= -cosmx/m  ∫cotmx dx = ln|sinmx|/m  ∫csc²mx dx= -cotmx/m…

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A: Given problem:- Find the number in the interval [0, 2/3] such that the difference of its square from…

Q: | 1) 2Ln(√x + 3) + 2Ln(√x − 1) = Ln(6x - 7) 2)3x+2 = 27

A: This question is related to solution of equations, we will solve it using given information.

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Q: Consider the function below. z²+4 z-2i z # 2i f(z) = (3 + 4i z = 2i Is f(z) continuous at z = 2i? If…

A: Let's solve.

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Q: *2t-h 5 if t=2 then h = -1 true O false O

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Q: (2x-1) dx 3 2x²³ -x²-27x +36 f

A: We can evaluate the given integral by using the method of partial fraction.

Q: Given f(x) = x² sec x, find f'(x). Ox² cos x + 2x sec x O x² secx tan x + sec(2x²) O 2x sec x tan x…

A: f'(x)=x2secx'         =x2'secx+secx' x2        =2xsecx+secxtanxx2

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Q: f(x) = 4x5 (12x² + 15x + 3)

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Q: Differentiate f(x) = (a-x)(a + x) with respect to x. Assume that a is a positive constant. f'(x) =

A: Solving the problem by finding the value of the differentiation.

Q: k 1. Find the value of in a. 0.298597 C. 0.498597 2. Find the value of a. 0.138629 c. 0.158629 k in…

A: Solution

Q: * What is inverse Laplace for 1 (s + 1)² + 1 y (s) =

A: option 2

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Q: Show that the operators T and T₂ from 2 R² into R² de fined by T₁: (F₁) √₂ ) → (9₂9₁) and T2=…

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Q: * Define this property L (f(t)eat) = F(s-a) Second shifting property O Linearity property O…

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