Find the limit (if it exists). (If an answer does not exist, enter DNE.) sin(9t), lim t-0 e5i + j+e4k 9t

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Q: EXAMPLE 9 Evaluate the integral. In (dr SOLUTION We let u = In(x) because its differential du = dx/x…

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Q: 5 x X LOS

A: Given: I=∫0πsin5x2cos7x2dx  ...1   As we know that; The Power rule: ∫xndx=xn+1n+1+C

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A: Given problem:- What is dy/dx for √(x + y) + √(xy) = 6 ?

Q: '글 +2+글 +5 The sum +8+ +11 written in sigma notation is equal to 8 3k-2 A k=1 2 8 3k - 1 B k=1 8 3k…

A: The sum 1/2 +2+7/2 +5+13/2 +8+19/2 +11.

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Q: Find the derivative, dy/dx: y = x² In x3 ý =- 2 1-4 ln x x³ In? x 3. ý = -2 In x – 2x | y = --(- 3…

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Q: 1 Which of the following is an antiderivative of the function f(r) = %3D 5+ x2 (a) 2x In(5+2?) 1 (b)…

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Q: Question 2 Differentiate the following function without simplifying y = arc sec(sec(02)) You may use…

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Q: Solve

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Q: Find the value of dy/dx at (1,0) of 2re" – In() = 4y² + 2a sin

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Q: 1. Solve the differential equation: xy' – y = 2x In x

A: Use linear differential equation concept

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Q: cos²(x) + 2cos²G) . cos³(x) - .dx

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Q: Attempt 3 A net is dipped in a river. Determine the flow rate of water across the net if the…

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Q: Find all the first and second partial derivatives of the function f(r, y) = x°y – 3y“. %3D

A: Given :f(x,y)=x2y-3y4To find : All the first and second partial derivatives of the function

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A: Local Extremum values:              Consider the function f(x,y) .For critical points , fx(x,y)=0…

Q: Given the function, x = 3 + Vx? + y² , find y. Vx² +y² - X y Vx² + y? - > ア= y Vx? + y² + x ア= y Vx?…

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Q: Find the volume of the solid that results when the region bounded by x=y^2 and x=4y+5 is revolved…

A: Given: To obtain the volume of the solid when the region bounded by x=y2 and x=4y+5 is revolved…

Q: 14. Evaluate L{e" cos(30)}. s-4 A) s - 8s +25 B) s - 8s + 25 4 C) s - 8s + 25 s+4 D) s - 8s +25

A: As we know that the Laplace identity; 1). If Lft=Fs then Leatft=Fs-a  2). Lcosat=ss2+a2   Given:…

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Q: x+dx Using trigonometric substitution, - (1+x²) = tan odo A sece sin*Ðd0 cose sec 8d0 tan 20 D None…

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Q: Find the following for the given equation. r(t) = 8 cos(t)i + 8 sin(t)j (a) r'(t) = (b) r"(t) = (c)…

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Q: Find V· (F x G), if F(x, y, z) = 6xi+j+15yk and G(x, y, z) = xi + yj – zk. V · (F × G) =

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Q: 1. Find all relative extrema and saddle points of the functon Use econd Partials Test where appli…

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Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

A: To evaluate the value of  ∫-∞∞7x2+4x+8dx=7∫-∞∞7x2+4x+4+4dx=7∫-∞∞7(x+2)2+22dx

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x + 3 lim x--3 x + 27

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Q: Consider f(x) = (5x + 11)2022, find: i. f'(x) ii. f"(x) iii. f''(x)

A: Given Data: f(x)=5x+112022 Formula used: dax+bndx=nax+bn-1dax+bdx dxndx=nxn-1

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Q: (a) / Which of the following integrals is equal to -2+ In 2? X - 4 dx (a) 4- I dx (b) 2 - 4 da (c),…

A: To find which of the given integrals has given value

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Q: 2.) S- e2x dx ex – 5

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Q: Find the second derivative [ f"(x)] of the given function: f(x) = eln Vx²+2 %3D (x2 + 2)) x(x² + 2)-…

A: Given problem:- Find the second derivative [f''(x)] of the given function:   f(x) = eln√(x^2+2)

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Q: Two numbers have a sum of 72. What is their product if it is a maximum? (A) 1296 B) 1297 c) 1298…

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Q: sion into quadratic form, ax² + bx + c = 0, and ide %3D

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Q: ||r(t) × r"(t)|| ||r(t)|| Use the formula k(t) to find k(t). 13 13: r(t) = t’i+ t³j K(t) =

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