Calculate the sum of the series a, whose partial sums are given. n = 1 n2 - 1 S. 5n2 + 1

Q: 2- 3x +8 2-X2C

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Q: Find F' () if F(x) = 2 cos¯1 Vx.

A: To find out the F'(1/2) 

Q: Determine the surface area generated when a portion of the curve in the first quadrant of y? = 1+ is...

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Q: Determine the surface area generated when a portion of the curve in the first quadrant of y? = 4 +x2...

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Q: Evaluate: sin ycos ydy. sinºy A siny +C 8. 6. sin y sinsy + C 8. sin°y sin'y + C 8. - 6. sin'y + C 8...

A: Here we need to solve the given integral .  

Q: Sketch a graph of the function y = 3x2 – 8x + 5. Use calculus to find: %3D a. increasing and decreas...

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Q: The graph shown below is Ax) = 2 cos x. If g(x) = Sðf(t)dt , find g '( ). %3D %3D 4 3 54 32 -14 1 23...

A: The function is given by fx = 2cosx The graph of the function is  To evaluate: The value of g'π if ...

Q: A company knows that the unit cost C and the unit revenue R from the production and sale of x units ...

A: Rate of change of unit cost is given as $9 /unit. Unit revenue=$2000 We will find the rate of change...

Q: Set up an integral that represents the length of the curve. = sin²(t), y = 1 –- 3 sin(t), 0 <t < T !...

A: The given problem is solved below.

Q: - The appropriate integrating factor for the following differential equation (2x + cosy)dx + (x²tany...

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Q: 1. Below is the graph of f (x) = |x|. Using the left side of the function with the equation y =- x, ...

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Q: nt Use A = P(1+– where: n A = the amortized amount (total loan/investment amount over the life of th...

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Q: - 1] Q2 a. Find the eigenvectors of the matrix b. Solve the ordinary differential equation: dy Y-e d...

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Q: You deposit $2000 in an account earning 5% interest compounded continuously. How much will you have ...

A: topic - exponential function

Q: Find the relative extreme of the function f (x) 12+2x+2 and where they occur.

A: Given: - The function is, f(x)=x+1x2+2x+2 To find: - The relative extreme of the given function.

Q: Which of the following is/are true of f(x) =(x+3)*at x = -3? A. Continuous at r=-3 B. Discontinuous ...

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Q: Evaluate: S,(3y6 + 8y* – 9y2)dy 2

A: Given query is to find the value of the integral.

Q: Find the domain and range of -4 < a<0, f(r) = 0 <r<4.

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Q: Find the equation of the tangent line to the curve y = x² – 5 if the tangent lir is parallel to the ...

A: we know that if two lines are parallel then their slopes are equalGiven that the tangent line is par...

Q: Which integral would represent the area shown below? The function is f(x) = 2x + 2. 8 6 4- 2- 0.5 1 ...

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Q: Question 3 Determine whether the improper integral converges or diverges. 14e5x dx A Diverges B Conv...

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Q: Using an appropriate substitution, (cos-1 (x) the integral S dx equals: V1-x2 -e(cos- (x) -elcos-1(-...

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Q: The values of C, and C, so that y(x) = C, e3x + C, e-3x satisfies the %3D following conditions: y(0)...

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Q: 6. - fycos ydy

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Q: Match the integral expression on the left to an equal expression on the right.

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Q: At which point/s (value/s of x) is the function continuous but not differentiable? -4 2 4 6 8 10 12 ...

A: function is not differential at point where either its not differentiable or it has sharp point on c...

Q: Find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2)

A: We will find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2) in the following s...

Q: 15. The following broken-line graph displays the depth of snow over a 2-day period. Depth of Snow 40...

A: To find out the rate of snow falling for first 6 hours. 

Q: Given the vector function. Calculates the principal normal vector N(t) when t=6.9

A: Question- Given the vector function. Calculates the principal normal vector N(t) when t=6.9 ?      

Q: . Find the first, second, and third derivative of function f(x) = 3x5 – 2x³.

A: Topic:- derivatives 

Q: Rewrite the following integral using substitution: s8 (1+3x)?dx

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Q: Find two unit vectors in 2-space that make an angle of 45° with 6i+ 5j. NOTE: Enter the exact answer...

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Q: Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile i...

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Q: Sketch the region enclosed by y = 4x and y 4x2. Find the area of the region. %3D

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Q: Find the equations of the tangent plane and normal line to the surface with equation 9y? + 9z2 = 22 ...

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Q: Solve the problem. A company knows that the unit cost C and the unit revenue R from the production a...

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Q: Consider the following function RX) - 9x - 7 Determine whether the function is even, odd, or neither...

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Q: tany Oメ

A: The given limit,      limx→0tan xsin 2x

Q: The solution of the non-exact differential equation (x*e +5dy + (1 +2x²e")dx = 0 is: O x^2 e*y+Inlyx...

A: To determine the solution of the following non‐exact differential equation.x3ey+xydy+1+2x2eydx=0

Q: Given F(x)=2f(xr)-8(x) and fS-1) = 2, f'(-1) = 3,9(-1) = -5,g'(-1) = 4, find F'(-1). %3D %3D

A: The detailed solution is given below Thank you 

Q: Evaluate: ,(3y6 – 8y* + 9y?)dy

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Q: Find 2x dA over the region R = {(r, y) | 0<z< 4,0 < y < 6} by identifying it as the volume of a soli...

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Q: Evaluate f'(-2) if f(x) = x* – 5+ x-2 + 4x-4.

A: The detailed solution is given below Thank you 

Q: A straight line perpendicular to and passing through the point of tangency of the tangent line is ca...

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Q: Let y = tan(5z + 6). Find the differential dy when a = 4 and dæ 0.1 %3D Find the differential dy whe...

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Q: Cansider the function. x) - 3x - 8 And the Inverse function of r. Slep 1 Let y- 3r-8, then solve or ...

A: The given function is; f(x)=3x-8.

Q: Which of the following best describes the function below? S (x)={* -4 ifx<2 Wr-2 if2sx if 2<.x A. Co...

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Q: Using an appropriate substitution, cos x-sin x the integral Jo cosx+sin x dx equals: 0 cosx+sinx 1 -...

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Q: 13 Which of the following is true about f(x) = [x]? A. The function is continuous at x = 0. B. The f...

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Q: Q1. Fill in the blank with a suitable mathematical expression. 1. The function f(x) is symmetric abo...

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