Σ n! n=1

Q: Given the differential equation: D´(sin x- cos x+ 3e* +x²) What is the fourth derivative? a - sin x+...

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Q: Assume that the integral / I f(z, y)dædy exists. 36 Which is the equivalent double integral with the...

A: Given that: ∫06∫-36-y236-y2f(x, y)dxdy

Q: Solve the following differential equations properly. a. xdx + (ydx - xdy) cos y/x = 0 ; when x = 1 ...

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Q: sinA (1+ cosA) prove that = 2cosecA (1+cosA) sinA

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Q: Solve the following linear differential equation y(6) – 64y = 0

A: Topic:- solution of differential equations

Q: F(x) = (x + 3)2/3 (a) Find the critical numbers of f. (Enter your answers as X = (b) Find the open i...

A: Critical number, increasing and decreasing interval, relative maximum and relative minimum

Q: Find the intervals over which the function is increasing and decreasing. (Use symbolic notation and ...

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Q: - 1 If f(a) = 5 tan 6 sin(2a)), %3D f'(x) =

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Q: sec x dy-4sin xsec ydx=0

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Q: 1 3. y' -- %3D xy+x²y3

A: See the details solution in below

Q: 7x2 + 6x + 2 If f(x) then: f'(x) = f'(2) =

A: The given function is f(x)=7x2+6x+2x

Q: In what degree of homogeneity is the function

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Q: 2. Solve the following Infinite Integrals. See if they are Convergent or Divergent. sin x dx V1– 2 c...

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Q: Explain how the graph of g is obtained from the graph of f?

A: First we have to draw graph of y=x2−4.

Q: Let g be a continuous function with g(2) = 5. The graph of the piecewise-linear function g', the der...

A: Note:- According to our Guidelines we can provide the solution of only 3 sub parts of a question ple...

Q: Evaluate the following expression. arccos Report your answer as a simplified fraction.

A: arccos(-1/2)  =>120°, 240 

Q: n-1 Find the fifth partial sum, S5 = E-, 4()" . Write as a fraction %3D reduced to lowest terms in t...

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Q: 4. An ordinary differential equation (ODE) is an equation that contains an unknown function y(x) and...

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

A: The given function is f(x)=ln(x), c=1

Q: Find the GS of: (r + sin e - cos e)dr + r(sin e +cos E)dO =0 O r2+2r(sine - cos©+C=0 Or2-2r(sine - c...

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Q: Which polar coordinate pair labels the same point as the one shown below? ..... Select all that appl...

A: As  x=r cosθ   and   y= r sinθ.

Q: 14. s(1 + VE)dt +tVE ds = 0; when t = 1,s = 1

A: Firstly , separate the given differential equation and after that integrate both sides.

Q: Determine whether the geometric series is convergent or divergent. 00 5n (-2)" – 1 n = 1 O convergen...

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Q: Q:Evaluate : [f(x)dx, iff(x)= V-* +1;*-13x<k,k = 1,2.

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Q: at ( – 3, 1). The equation of this tangent line can be written in the form y = mx + b where m is: wh...

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Q: An office supply company sells x permanent markers per year at p dollars per marker. The price-deman...

A: a) Demand : p=10 - 0.001x Cost : C(x)=5000+2x Revenue=Price * Quantity So, R = px To maximize revenu...

Q: The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing (in mm3/...

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Q: Find the area of the shaded region bounded by the x-axis and one arch of the o dx dt.) dt below. (Hi...

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Q: 5. Integrate using Rational Functions: xp: (x+ 1)³`

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Q: (Give your answer in the form of a comma-separated list. Express numbers in exact form. Use symbolic...

A: In this question we will use basic of calculus i.e application of differentiation. We will find crit...

Q: (a) Compute fxdx + ydy + (x + y – 1)dz where C is the line segment from (1, 1, 1) to (2, 3, 4). C 1 ...

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Q: (a) Let 7 : [a, b] → R" be a curve with 7' (t) # 0 for all t e [a, b]. Let s = s(t) be the arc-lengt...

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x + = - [0....

A: For absolute minimum and absolute maximum value of function , calculate the value of  function at en...

Q: d?y at this point. dx2 Find an equation for the line tangent to the curve at the point defined by th...

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Q: [2 -1 B = 1 -1] find If A = [3 0] |2 3 (а) А' B' (с) (AB)' (d) B'A'

A: Since we are given with the multiple number of question and our guideline is solve first question ki...

Q: (b) Let F be the vector field F = (ye™y + cos x, xe"y + ). Let C denote the portion of the curve y =...

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Q: Solve this. O. Find the equation of the curve whose slope at any point is equal to (-(y+1))⁄((x+1) )...

A: Let's find. 

Q: The graph of f(x) = +5 is shifted left 4 units, stretched vertically by a factor of 8, reflected abo...

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Q: What is the amplitude and period of the function shown below? 95 AMA 8. 5- 4. 3. 2- -4 4 -1 -2- -3. ...

A: topic - amplitude and period of function amplitude - the maximum distance moved by  wave measured fr...

Q: Which of the following is a proper substitution to solve the following Bernoulli's equation? zy'- 7e...

A: To find the proper substitution to solve the following Bernoulli's equation:xy'-7exy3=11y

Q: Find f[g(x)] and g[f(x)] in the following. -4 f(X) =x+7; g(X) = g(x)]= g[f(x)] = |

A: topic - functions

Q: 1. If n is an integer, then 2n +1 is odd.

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Q: (c) Let f(x, y, z) = xyz cos(x). Compute the gradient field of f.

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = In(x2 + 5x ...

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Q: 6. A projectile is launched with an initial speed vo at an angle 0 (here 0 <0 < 7/2). The height as ...

A: **As per our guidelines we are allowed to answer maximum 3 sub-parts at a time. Kindly please re-pos...

Q: SOLVE THE FOLLOWING DIFFERENTIAL EQUATION PROPERLY:  a. x2dy + y2dx = xy(xdy - ydx) b. (z + z3)dx ...

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Q: Evaluate the double integrals by changing to polar coordinates, where Ris the region bounded by y = ...

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Q: [ (x)dx, iff (x)= Vx -k+1;k-13x <k,k = 1, 2,.

A: We will solve using substitution

Q: The area bounded by the curve is 9y = x⁴ the line is y-9, and the y-axis is revolved about the y-axi...

A: Even if you revolve, the x coordinate of centroid wil be affected but y coordinate of the solid will...