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Q: Write the sum using sigma notation: A 7+ 10 + 13 + 16 + ...+ 49 = > B, where n=1 A B =

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Q: Solve the equation .11 y" + 3y' + 2y = x2

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Q: What is order of the equation 2y" + 2y' +3 = 0 Second order O Third order O First order O Zero order…

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Q: dy 3y- + 4x = 0 dx

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Q: Express the following sums using sigma notation. a. 4 + 5+6+7+8 b. 6+ 12 + 18+24 +30 +36 c. 12 +22 +…

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Q: This equation is. . .differential equation dy y2 = X x² + dx ху Bernoulli Separable Homogenous…

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Q: 3. A curve has equation y = Find the x-coordinates of the stationary points of the curve in the tan…

A: To solve the following problem

Q: Find the greatest and the least values of the function y = x³ – 3x +3 on the 2 (a). interval [-, ).

A: Solve the following

Q: Let y = 3x2. Find the change in y, Ay when x = 2 and Ar 0.2 Find the differential dy when x = 2 and…

A: We have to find solution

Q: 5 (b). ( the base radius making the surface area minimum. ) Consider a cylinder having fixed volume.…

A: Use the application of derivative to minimise the surface area.

Q: 6 sin(x)dx

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Q: Cyndee wants to invest $50,000. Her financial planner advises her to invest in three types of a…

A: answer is in next step

Q: - 4× dx хе

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Q: 1. It is a list, or an array of numbers arranged in a definite order. a. ordering C. arrangements d.…

A: Ans 1.       A sequence is a set of numbers  arranged in a definite order. and the numbers in the…

Q: Given the curve y = x' and the line y = 2 – x. Find the area of the region bounded by the curve and…

A: Area bounded by the curve y=x2 and the line y=2-x

Q: Find all critical points of the function f(x) = x³ - x? – 54x + 6. (Use symbolic notation and…

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Q: How to identify if the problem is integration resulting to inverse trigo. or trigo. substitution.…

A: To give an example of the integration where trigonometric substitution is possible.

Q: Given that Vf(15, -6) = 4i – j, find the directional derivative of the function f at the point (15,…

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Q: (-3,-).* Plot the point whose polar coordinates are (-3, . In the graph below, use the options to…

A: Given problem:- Plot the point on graph whose polar coordinates are (-3, -π/6)

Q: Given the curve y = x´ and the lines y = 0 and y = 2 –x. Find the abscissa of the centroid X of the…

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Q: Show that fu,, u2, uz) is an orthogonal basis for R. Then express x as a linear combination of the…

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Q: For the given points A, B, and C find the area of the triangle with vertices A, B, and C. A(4,7,2),…

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Q: Use symmetry to evaluate the following integral. 1 (6-x) dx | -1

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Q: f(x, y) = In (x²y - x) %3D

A: Here, the given function is: f(x,y)=ln(x2y-x) First to find the first derivatives:…

Q: Determine the equation of the tangent plane to the surface z = cos(x + 2y) at the point (2,-1,0).

A: Tangent plane to f(x, y) at (x0, y0) is given by below:

Q: |2 tan(x)dx

A: I am attaching image so that you understand each and every step.

Q: Solve the equation .11 y" + 3y + 2y = x2

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Q: Given the curve y = x´ and the line V = 2 – x_ Find the abscissa of the centroid * of the region…

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Q: 9. sin ở In(cos 0) de

A: let I=∫sin θ ln(cosθ) dθ Integration By parts: ∫udu=uv-∫vdu u=ln( cosθ) ; du=1 cosθ-sinθdθ=-tanθdθ…

Q: Find the volume generated by revolving the region bounded by y = - cos x and y = 0, from x= - 2x to…

A: Here, the curves y=-cos x & y=0 from x=-2π to 2π revolved about the x-axis.

Q: Find the area of the shaded region. 24) f(x) =x3 +2x2- 3x, g(x) = 0 -4 -3 -2 -1-1 4 -5 47 A) 12 81…

A: Topic = Area

Q: Solve the initial value problem.

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Q: of of For the function f(t,a) = sin (5t + 8a), find and at da

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Q: Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 13…

A: Let, x be the number of food cartoons and y be the number of clothing cartoons. Then maximize…

Q: Find all zeros of f(x) = 4x° – 20x² + 36x – 24. Enter the zeros separated by commas. Enter exact…

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Q: Find the slope of the tangent line to the curve r = 5 cos(0) at the point specified by 0 Preview 5/3…

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Q: 135 5. y = x³, y = x + 6, and 2y + 2 = 0 (Answer: S. u.) 4

A: The region bounded by the curves y=x3, y=x+6 & 2y+2=0 is:

Q: An open box is to be made by cutting small squares from the corners of rectangular board and then…

A: let "x" be the length of the side of the square cut.Length= 8-2xWidth = 6-2xHeight =xVolume =…

Q: Given a, b e Z, 6 7 0, consider the following affirmations regarding Euclides's algorithm: i) There…

A: We want to choose the correct option.

Q: G(x) = Si tan t dt Find G(1) = Find G'() =

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Q: 1. The line segment from (1, –1,3) to (0, –3,1) forms a diameter of the sphere S1. Find the…

A: Given problem:- The line segment from (1,-1, 3) to (0, -3,1) forms a diameter of the sphere S₁. Find…

Q: answer

A: We will find the particular solution.

Q: dr J. (z+1)?

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Q: Find the slope of the tangent line to the curve – 2x? + 4xy + y³ = 8 at the point (4, 2).

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Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = e=², y =…

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Q: dy 16t dt

A: answer is in next step

Q: H.W. 1. Find the arc length of the curve x = (y + 2)/2 from y=0 to y=1

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Q: Find the length of the curve y ' = 8x from x=1 to x = 8 www

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Q: Evaluate the integral using integration by parts. 5x dx= %xp

A: solving by integration by parts

Q: pose g is a function which has continuous derivatives, and that g(5) = -3, g' (5) = 3, g"(5) = –1,…

A: We have to taylor polynomial of degree 2 and degree 3.