Which of the following is undefined? cot() 131 A B sec(630") tan(-14n) D csc(-810")

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) COS X dx (sin x)20

A: Given, ∫cosxsinx20dx We have to evaluate the indefinite integral.

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A: This question is based on diffrentiation.

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Q: Find V x (V × F) if F(x, y, z) = 9xyj+ 6xyz k. V x (V × F)

A: WS have to solve the vector

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Q: Question 4 Determine the derivative of the given function: y = (e + e*)3 Oy = 3(e+e) (e" - e) Oy =…

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Q: arcsin = ab? x? - Va2- y2: Find y'. 2abe (+0) /a-y 1-y 2ab a 1-y 2ab a /a-y %3D

A: We neee to find derivative of y for the function given below:

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: What is the absolute maximum and absolute minimum of the function f(x) = x3 – 3x2 – 9x – 6 in [0,5]?

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Q: Find the general solution to the following equations. dx dy 1. + y = x , = 3y dt dt

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Q: Solve

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

A: Use linear differential equation concept

Q: Question 3 Determine the derivative of In(csc x) cot x Csc I - cot x CS z Previous

A: A detailed solution is given below

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:…

Q: EXAMPLE 6 Evaluate the following integral. tan (r) dr SOLUTION First we write tangent in terms of…

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

A: In given problem we have to find out relative minimum of given function for which first we find out…

Q: d Calculate r1(t) · r2(t)] and dt d [ri(t) × r2(t)] first by differentiating the product directly…

A: Given that,       r1(t)=9t i+4t2j+5t3k,   r2(t)=t4k

Q: A A A A A A A A A A AA A A A A A A A A A A A A A A A AAA 6. What is the sum of the series TC + ... +…

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Q: 1 Find the area onclosed by the Curve r=4-3 sin 0.

A: Area

Q: 2. Find the Area bounded by the curve y=4-x2 and the x-axis.

A: 2. The area bounded by the curve y=4-x2 and the x-axis Note:    Multiple questions are given, we are…

Q: Find the first derivative of the function below: f(x) = arctan(sec(x ))

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Q: 1. The study of integrals in calculus is motivated by the problem of calculating (a) the slope of a…

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Q: dx 2.) S 4+ x2

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Q: cos 6x cos 2x dx

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Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). r(t) = e"i+ e¬'j K(t)

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Q: 3. Differentiate. SET A. y = 3 cos(5x2 + 2)

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Q: Refer to the given below. Find the indefinite integral. Simplify your final answers (Just like how…

A: i)∫(2x3+12x2-5)dx=∫2x3dx+∫12x2dx-∫5dx                                   =2∫x3dx+12∫x2dx-5∫dx…

Q: Use power series operations to find the Taylor series at x = 0 for the following function. x -2+2…

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Q: integrate dx/(x²+x)(x-1)²

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Q: Find the Maclaurin series for f(r) using the definition of a Maclaurin series. [Assume that has a…

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Q: Find the arc length of the graph of r(t) eV2li +e¬V2lj+2tk, 0<t< v2 ln 9 NOTE: Enter the exact…

A: Given problem:-

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 6 cos(t)i +6 sin(t)j+…

A: As we know that; The expression for the curvature; κ=r't×r''tr't3 And The expression for the radius…

Q: Find all refative extrema and saddle points of the function. Use the Second Partials Te f(x, y) = x…

A: Here,  we have given a two variable function and we have to find out all the relative maxima and…

Q: 422+3r-2 Given z+1 determine y" 18 (z+1) (z+1) 2 (z+1) 10 (z+1)

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Q: Find the distance between the two parallel planes 5x – 3y + z – 2 = 0 %3D -10x + 6y – 2z + 3 = 0

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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: - 4g° + 1000g, where R(g) is in dollars Suppose a product's revenue function is given by R(g) g is…

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Q: x² – 2 (x + 2)(x + 1)²

A: Partial fraction

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Q: 3. If g(x) = -dt, find g'(2). %3D

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Q: S- 3 dy 3y - sin –+C 4– 9y2 3 A True B) False ||

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Q: Find div F and curl F if F(x, y, z) = 12y"2³i – 3x"z+j – 4xy°k. div F= curl F=

A: A detailed solution is given below

Q: sec" /x dx 17. 2 5n Ans. 6

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