tio test for absolute convergence to determine whether the series co te

Q: Find the inflection points of each of the given curve.  3y = x3 + 3x2 – 9x + 3

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Q: ax ve

A: To evaluate: I=∫dxex...(1)

Q: If x2 + y2 = 100 and dy/dt = 4, find dx/dt when y = 6. (Enter your answers as a comma-separated list...

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Q: sin xV1 cos xdx

A: ∫sinx1-cosx dxSubstitute t=1-cosxt=1-cosxDifferentiatedt=sinx dx

Q: Find the derivative of 7 (t) = (1+t°, te¯t, sin (2t)) A. F'(t) = (3t°, (1 + t)e¯t, 2 cos (2t)) B. 7(...

A: We are asked to find the derivatives.

Q: В. up to 6 decimal place. Then, answer the corresponding question in each number. Evaluate the follo...

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

Q: Solve the given differential equation. All solutions should be founc 3x? – 4y – y 4x + 3xy? dy | dx ...

A: Follow next step

Q: dx V4x – x2

A: Given function, It can be solved by converting denominator Into (x-2)2 form Then by substituting  u=...

Q: A point (5, - 1) on the terminal side of an angle 0 is given. Find the exact value of sec 0. 2/6 3/2...

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Q: Consider the region R bounded between y=x2-4x and y=-x2+2x  Set up an integral for the area of the r...

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Q: Find all the maximum and minimum points of f(x) = x4 – 8x2.

A: As we are not given any particular, we will take the help of the graph here.

Q: Use the appropriate limit laws and theorems to determine the limit of the sequence. in an = sin (Use...

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Q: 3 аx2а (x2а +1)" dх a:

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Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = xo and then find the nth Taylo...

A: Given :   f(x)=ex x0=6

Q: The volume of a right circular cone of radius a and height y is given by V : ' = ma²y. Suppose that ...

A: From the given problem; The expression for the volume of the cone is: V=13πx2y And The volume of the...

Q: Find the solution of the given initial value problem in explicit form. sin(2r) da + cos(6y) dy = 0, ...

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Q: Find the slope of the line tangent to the graph of f(x) = 3x² - x- 5 at x = 1. %3D Provide your answ...

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Q: Find the Taylor polynomials of orders n = 0,1,2,3, and 4 about x = x0, and then find the nth Taylor ...

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Q: If f(x, y) = x cos y + ye", find dydx

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Q: Let sk En(0.1)" n=1 Find s9.

A: Given that sk=∑ n=1k n (0.1)n -(i) Our Aim is to find s9=?

Q: A trough is 3 m long, 5 m wide, and 4 m deep. The vertical cross-section of the trough parallel to a...

A: Base on the general formula of the work we will calculate the total work required for pumping fluid ...

Q: 1. Given f(x)= (a) Show that f'(x)= 2(x² -16) 3x by using the quotient rule. Hence, find all 11 the ...

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Q: S(x+)* dx- X.

A: Given: I=∫x+1x2dx   We know that; The Power rule: ∫ax+bndx=ax+bn+1n+1+C ; n≠-1 And The sum/differenc...

Q: 10. Using the method of undetermined coefficients, write the form of the assumed particular solution...

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Q: S (x +) dx 2 X.

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Q: For the next six questions, consider the differential equation: y" + 4y = g(x), g(x) # 0

A: Let's find. 

Q: Evaluate the following integrals. 1. sec-a dæ cos Va dx Væ csc /æ 2. x2 dx - 3.

A: Integration by parts

Q: Evaluate the following integrals. 1. 4.x3 sec-1 æ dx cos VT dx x Csc Vx 2. dx V4x – x2 3. -

A: Given problem:-

Q: A certain drug is being administered intravenously to a hospital patient. mg Fluid containing 5 cm3 ...

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Q: Use the graph of f(x) shown below to determine each of the following limits. If any of the limits do...

A: Let's find. 

Q: 10. Romeo is walking towards North at a rate of 4m/s. Ten seconds after, Juliet walks towards East a...

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Q: Three curves that describe the motion of a particle along a coordinate axis at time t (in seconds) a...

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Q: Given f(x) = Vx+ 8, find f' (-4) using the definition of a derivative. %3D Provide your answer below...

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Q: Evaluate the following integrals. 1. 4x sec .3 -1 x dx

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Q: Evaluate the integral below by following the steps given. 1 xp= x2 I || 6/ a.) Show that the substit...

A: Given: I=∫19-x2dx  ...1   As we know from the trigonometric identity: sin2θ+cos2θ=1 And ∫a·fxdx=a·∫f...

Q: [2x+5y=7 3x + 2y = -6' 1. Solve the linear system using graphical method.

A: The given linear system,2x+5y=73x+2y=-6

Q: 5. Given that r(t) = 3i + e* sin tj + e cos tk Find equations of the normal plane and osculation pla...

A: We have to  find equation of normal and oscillating plane of above curve. 

Q: Items 15 The graph of a function f is shown. On top of the graph of f, sketch the graph of f'. Use a...

A: The graph of the functions are given as 

Q: (2 x* y? + 4x² y + 2 x y² + xy* + 2 y) dx +2 (y³ + x² y + x) dy = 0

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Q: 1+cscx h(x) =- 1-csc x

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Q: Determine the approximate root (x_r2) of the f(x) = 0.35x^4+2x^3 -x^2+0.36x +4, upto 2 iterations us...

A: f(x) = 0.35 x4 + 2x3- x2 + 0.36 x +4 f(-2) = -9.68 < 0 f(0) = 4>0 Hence, a root lies between -...

Q: Which of the following is the general solution to the differential equation ydx – (x – Jx² + y? )dy ...

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Q: Find the area of the cardioid r=2(1+cosθ). a. 2π b. 4π c. 5π d. 6π e. none of the above

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Q: Find r(r+ 6)° dx. A 12r²+C B 5x5 + 3x*+ 12x³+C

A: Using integration rules & formulas.

Q: Question

A: We will find the value of sin theta. 

Q: 4. Given that r(t) = cos ti + sin tj + In cos tk Find the curvature k and vec- tors T, N, B at the g...

A: Find curvature at t=1

Q: Name the quadrant in which the angle 0 lies if cot t > 0 and sint < 0. O II OIV O Not possible to de...

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Q: Compute the first 6 terms of the sequence {an} where An-1+n a1 = 1 and an for n > 2.

A: The given sequence,a1=1 and an=an-1+n2 for n≥2

Q: A large cylindrical tank has radius 2 m. Water flows out of a tap at the bottom of the tank at a rat...

A: radius of tank = 2m initial depth = 9m depth after 15 minutes = 4 m  

Q: What is the y-intercept of the function y = cot I? || ㅇ(T,0) O (0,0) O (1,0) (0, 1) O It does not ha...

A: The function is given as y=cot(x) The objective is to find the y-intercept.