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Q: Evaluate the integral [[(ate?) i+ (o-8) j+ (3) k]at 0. S[(t022) i+ (e-) j+ (3)kJat = i+ ()j+ ( )k (T...

A: The integral,      ∫014te2t2i+e-3tj+3kdt

Q: Find the derivatives of the following functions: 1. y = 2x3 + 6x 2. y = 7x* - 3x? 3. y = (3x +1)(2x ...

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Q: S sin 8x sin x dx O - 0. 02 O - 0. 01 O 0.02 0.01 O O O

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Q: The cross product is not associative. (It is not necessary for | a xb |x c X c to be the x c |.) Fin...

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Q: E. y = xArctanx - In V1+x

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Q: Two carts, A and B, are connected by a rope 39 ft long that passes over a pulley P. 12ft B The point...

A: Rate of change

Q: Evaluate the integral by changing to cylindrical coordinates. V16 - x 2 16 - x2 - y2 4 x² + y² dz dy...

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Q: (1+4er²)(3-e+²)x er2 dx

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Q: Find the volume of the pyramid with base in the plane z = -1 and sides formed by the three planes y ...

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Q: Find the critical point/s of the function f(x,y) x³+2xy-2x-4y

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Q: 17 Find the exact value of cos20 given csc0 and -< 0 < TI 8.

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Q: 2 + x², -2 < x < 0 f(x)dx; f(x) TX + 2, 0<x<4 21 -2

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Q: tf(r.,2) 4ry t and u is the unit vector in the direction of (4, 2,-5), tmen the drectional denvative...

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Q: A particle moves along the x-axis so that at time t > 0 its velocity is given by v(t) = 3t² – 30t – ...

A: topic - quadratic equations

Q: Find the volume V of the solid S that results when the region bounded by y = x2, y = x, x = 0 and y ...

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Q: Find (f-1)'(a) for f(x) = ーX-3 when a = 3x +2 (Enter an exact answer.) Provide your answer below: ((...

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Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 – 3y², and the plan...

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Q: 1. Determine if if r2 /2r is differentiable at r 2.

A: First check for continuity then the derivative if both exist then function is differentiable. 

Q: Which of the following integrals represents the area of the surface obtained by rotating the curve y...

A: The curve y=lnx, 1≤x≤3, rotating about x-axis

Q: 1. (a) Plot the first four terms of the sequence 3n2 – 3n + 2 n=1 (b) (i) Write in bracket notation ...

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Q: Use the second partial derivative to Find the relative extrema OF the Function f (x, y) = x°t 2xy-6x...

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Q: x3dx 3. S (x4+4 )4

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Q: Given the triangle below, find sec(0). Enter an exact answer in fraction form.

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Q: 2. f(x) 3. f(x) = (56x – 3)(4x +5) = 56x - 32x + 16x - 10 4. f(x) = 2x-6 x+3

A: since you have posted multiple question in this question which are not interlinked so i have solved ...

Q: ( 2 + x², -2 <x< 0 4 f(x)dx; f(x) = 1 ·x + 2, 1. 0<x< 4 -2

A: ∫ xn dx = xn+1n+1 +C ∫ab f(x) dx = ∫ac f(x) dx + ∫cb f(x) dx , where , a&lt;c&lt;b.

Q: Show detailed solution for all. a) Provide the Maclaurin series expansion of f(x) In(3 – 2x) b) Find...

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Q: A Construct the perpendicular bisectors of the following segments. B. Construct the angle bisectors ...

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Q: Given g(x) = 3x-1 – 2 A) State the parent function f(x) = %3D B) Describe the transformations: Confi...

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Q: Write an equation for the line through center a circle (x2 + y2 + 4x+6y = 3) which make an angle) wi...

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Q: Solve the differential equation by using integrating factors. y' = 6y + 5 y(x) =

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Q: dx sin? - cos 2

A: Here, the given integral is: I=∫0πsin2x2cos7x2dx Substitute x2=t⇒x=2t⇒dx=2dt as x→0⇒t→0 &amp; as x→π...

Q: Evaluate the series or state that it diverges. 00 3 Σ (0.4)*. k= 0 ... Select the correct choice bel...

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Q: sin x + 10(csc x)² dx

A: To compute: ∫(sin x+10(csc x)2)dx

Q: IV. Determine whether the given series is convergent or divergent. Justify your answers (a) E (c) E(...

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Q: I Eliminate the arbitrary constants -2x 2X Y = C,e cos 2× + Ge sin 3X

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Q: 2e3+6 + x Evaluate lim x-2 and write your answer in simplest form. 2x +4

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Q: Suppose that a population grows according to the unlimited growth model described by the differentia...

A: Question: Suppose that size of the population grows according to the unlimited growth model describe...

Q: 4. The derivative of f(x) = ln x at x = 3 when hpresent = 0.001 and hprevious = 0.002. %3D 5. The de...

A: f(x)=ln xhprevoius=0.002f'(x)=f(x+h)-f(x)hf'(3)=f(3+0.002)-f(3)0.002f'(3)=ln(3.002)-ln(3)0.002f'(3)=...

Q: Find the area of the surface obtained by rotating the curve y = 5x° from æ = 0 to æ = 9 about the x-...

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Q: 3. Sketch the region bounded above by the curve y = x², below by the line y = -x – 2 and on the side...

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Q: -6 -5 4 The plot above is created with the parametric equations S¤(t) = a cos(bt) y(t) = c sin(dt) T...

A: Solve the following

Q: 13 2 3 Find the exact value of sin20 given cos0 = and < e < 2n Find the eract value of cos?A givon c...

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Q: This exercise uses the population growth model. A culture starts with 8300 bacteria. After 1 hour th...

A: Since you have posted multiple questions I can do first question as per our company guidelines pleas...

Q: Σ cot n=1 converges or diverges. You have to use the Limit Comparison Test to justify your answer.

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Q: siny Given the integral S" S" dy dx, Sketch the region of integration, reverse the order of integrat...

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Q: B. . .] For each of the following limits, use the properties of limits to compute the limits. Show y...

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Q: 3 A bicycle wheel rotates 400 times per minute. If the rider removes his feet from the pedals, the w...

A: The objective is to find how many times the wheel will rotate in the eighth minute.

Q: Find the point(s), if any, at which the graph of f has a horizontal tangent line. f(x) =  x2 x − 5 s...

A: We have to find the point at which the graph of f has horizontally tangent line

Q: Question 1 Find the derivative of g(x) = 3 cos™' (x) at the point x = 4 %3D %3D (Enter an exact answ...

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Q: 3. Solve the following equations over all real num V2 sin(-x) + 1 = 0 a. |

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