Evaluate the definite integral. NOTE: Enter the exact answer. 10 | ² || = [ i+t²j||dt

Q: Solve the following differential equations of -x 2y" - 2y + y = 2e¯*

A: If the roots of the auxiliary equation are complex α±iβ , then the complementary function is…

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Q: fe²x+Inx² sin x² dx = e2x cos x² dx

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Q: 5. Given: G(x, y) = 4y¹ sin(2x³) Gyxy(x,y). What other 3rd order partials are equivalent to Gyxy(x,…

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Q: Given: (1 + 2x) e-x dx. Using integration by parts and letting u = -1-2x, dv = f(x)dx, then the…

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Q: Compute the quadratic form x Ax for A= Xx₁ 12 - a. x = b. x= 1 X2 a. x¹Ax= 3 2 [1] 10 C. X = and…

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Q: C. y = 5x² + 2, x=0, x=2, y = 0

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Q: S 1 xvx²-2x dx = √x²-2x X +C

A: To prove that ∫1xx2-2xdx=x2-2xx+C

Q: f/²sin (co COS () sin (²) dx (Consider initially the first 2 terms) ATT/A a dr

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find F'(x). 1. F(x) = √x+² (4t + 1)dt 2. F(x) = f*t³dt SOLUTION IN HANDWRITTEN

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 1+ 1. lim. 2-12x²+x-1

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 3. lim (x-3) tan(9-x²)…

A: Formulas of limits which have been used are written in the solution

Q: A= and B = . Find a vector perpendicular to both A and 2A - BO O O none of the above

A: A vector perpendicular to A and B is :  C = A x B

Q: Using trigonometric substitution to solve: sin 2x + C 8 cos x√3-cos²x sin 2x 4 cos x√4-sin²x secx 8…

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Q: 15x²x³43x - 19 The integral (x + 1)²(x² - 6x +13) Ax + B What is the value of x²+bx+ca -dx? 3 A…

A: This is a problem related to integration. Based on the concept of partial fraction decomposition we…

Q: π/4 x³ dx (x²+4)5/2 ST/4 (Use trigonometric substitution)

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Q: 3. lim x-3 (x-3) tan(9-x²) sin²(2x - 6)

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Q: 19. Evaluate the following sin³ [sin³ (2) cos(4) dx 32 A. 35 COS 5( 4 ) [-5cos² (4)+7] -cos 32 32 -…

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Q: 27 If (2x 3) [133] [3] 3] -3 23 1. 2 13 2 2 3. 13 2 23 2 - 0, then the value of x is

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Q: 7. f(x) = 3√x; [1,4] 8. f(x) = x-2/3; [1,27]

A: We can solve this as follows:

Q: 1o. 1 |x-3|dx

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Q: Your company manufactures Laser Firing Aardvarks M for sale to the general public. The cost, in…

A: We have to above the question

Q: Consider the parabola given by the equation: Find the following for this parabola: A) The vertex is…

A: The given equation,    fx=-9x2-18x-7

Q: = Find area of the region bounded by x² + y² = 4², 10y = -6x and 13y 8x where y > 0. Leave your…

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Q: 12. -s-7 (s+1)(S-2)

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Q: Let T: R³ → R³ be a linear transformation such that T(1, 0, 0) = (4, -1, 2), 7(0, 1, 0) = (1, 3,…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Determine the values of r for which the differential equation y' +9y = 0 has solutions of the form y…

A: Given differential equation.

Q: NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time…

A: Given; h(t)=-4.9t2+91t+164

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: -π/4 x3 dx (x²+4)5/2 (Use trigonometric substitution)

A: We have to solve above question useing trigonometry substitution

Q: Use linear approximation or differentials (but not both) to estimate: cube root of 7.98 Is your…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the particular solution of the  differential equation with the initial condition given below.…

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Q: r₁(t) = cos(t)i + sin(t)j +5tk, r₂(t) = 4i + tk X d -=[r₁(t) · r₂(t)] 10 t - 9 sin(t) = dt d -[r₁(t)…

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Q: VI. Write TRUE if the statement is correct, otherwise write FALSE. There is no need to justify your…

A: 1. True 2. True

Q: Find the curvature and the radius of curvature at the point t = 0. x = et cos(t), y = et sin(t), z =…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 1 + ²/ 1. lim x12x² + x1

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Q: [₁x³√x² + 3dx x-3 2

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Q: Find Duf at P. NOTE: Enter the exact answer. Duf= f(x, y) = sin(3x – 4y); P(4,3); - = u 3 i

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Q: e3-6-2, if x 3 = 3. 1. Determine if f is continuous or discontinuous at x = 2 and x =

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Q: Question 9 Using trigonometric substitution to solve: cos x dx f 3 (4-sin²x)2

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Q: Question 3 x²+x+1 Sa 2x²+2+x³+x -D Sa x+2' - dx = [Aƒ (x) — B ln(g(x)]å + D rb dx 2 and if A = B<0,…

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Q: Solve the differential equation and simplify (D^3 + D)^2y = 0

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Q: c. The region R enclosed by the curves y = x and y = x² is rotated about the line y = 2. Find the…

A: Using disc method, volume of solid is evaluated.

Q: The general solution of y' = Y can be written in the form = C

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Q: II. Find Do not simplify your answers. da 1. log, (√2x² + y) + tan(x² − ³) = sin¯¹ (2² − 1) + 2

A: log3(2x23+y )+tan(xπ-πy)= sin-1(x2-1)+π21log(3). 2x23+y 23×23x-13+y'+sec2(xπ-πy).(πxπ-1-πy.…

Q: Find all real solutions of the equation 2g² = 50. Write your answers as a list, using a comma to…

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Q: 15x²x343x - 19 The integral (x + 1)²(x² - 6x +13) can be rewritten as Slax [ax² + bx² + c + (mx +…

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Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: We have to solve above question and find preimage function

Q: I-1² ( ²7 ) ₁_²01|1 - 1² || lim, 07

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Q: The phone company A Fee and Fee has a monthly cellular plan where a customer pays a flat monthly fee…

A: answer is in next step