up 1. √ √2x + 1 dx

Q: fz² dz along the indicated paths: -1+i -1 C 0 (a) 1 1 + i 17 0 (b) 1

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Q: Reverse the order of the integration ² dy dx + 2 dy dx equal:

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Q: (d) Let an = 6n²+ n-1 ntn and bn √n n+1' (i) Determine whether {an} is convergent or divergent.…

A: Given;  an=(6n2+n-1) /(n2+n)  bn=sqrt(n)/(n+1)

Q: Find the indefinite integral: O 10sin 3x - 20 cos 2x +6 e5x + C 90sin 3x 60 cos 2x + 150 e5x + C…

A: The objective is to find the indefinite integral.

Q: 2. Find the area of the region between the curve, x = y² + y −6, y- axis and y=0; y = 3.

A: we need to find the area bounded by the given curves.

Q: 1 2. Lim x0x 1 sin x

A: Given:      limx→0+1x-1sinx simplifying we get     =limx→0+sinx-xxsinx Apply L'Hospital's Rule:…

Q: e. Find the second derivaitve. f''(x) = = f. Use parts b through e to identify maximums as points.…

A: e.fx=2x3+3x2-36x-54f'x=6x2+6x-36f''x=12x+6f. for maximum point f'x is +ve to…

Q: Use implicit differentiation to determine dy dx = dy dx given the equation x² + y5 = 3.

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Q: 3. The angle between vectors A = 91-j+5k and B=(-2,7,1) is... ***** 16- 12 4. 2) shor mis

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: (c) Express the number 1.234567 as a fraction (in its simplest form) using the sum of a geometric…

A: Ans=45679/37000 For detail...go through the solution.....I have solved step by step in detail

Q: Find the centroid of the region bounded by the semicircle y = √a² -C O (0,5/4a) O (0,4a) O (0, a)…

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Q: [e²y ycos (xy)] dx + [2xe²y XCOS (xy) + 2y] dy = 0

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Q: 2. fizə] ycos (xy)] dx + [2xe2y - xcos (xy) + 2y] dy = 0

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the area bounded by the following functions/lines/curves: f(x) = 3x3 - x2 - 10x; g(x) = -x2 +…

A: Given: f(x) = 3x3 - x2 - 10x; g(x) = -x2 + 2x Let's first find the intersection point  3x3-x2-10x =…

Q: Problem 2: Use the definition of the Laplace transform to find the transform of the piecewise…

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Q: Find the lower sum for f(x) = +4 on the interval [-4, 0] using 2 rectangles. 10 "F Submit your…

A: Here we have to find the left sum of given function.

Q: Use the trapezoidal rule with n = 20 subintervals to evaluate I = -5 sin² (√0× t) dt

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Q: The region in the first quadrant bounded by the graph of y=8-x¹2, the x-axis, and the y-axis is…

A: The region in the first quadrant bounded by the graph of y=8-x32, the x‐axis, and the y‐axis is…

Q: Q4: If f(x,y) = x²y +exy Siny Find 1) 2) (D = f) at po(1,0) in the direction of 0 = Po

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Q: A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution…

A: We are given that in a 200 gallon tank , intially there was 100 gallon of water which contains 20…

Q: The water level inside a cylindrical tank (height 12 ft) is 2 ft below the top of the tank. If the…

A: Explanation of the answer is as follows

Q: 5. Evaluate using the circular disk method. Find the volume of the solid formed by revolving the…

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Q: - S(2 + 5x) es dx

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Q: s={ 3112 4'2'3'9' =(5, 5.5, 6, 6.5, 7, 7.5,...} = {√2,2√2,3√2, 4√2,...} ={√2,2,2√2,4,...}

A: Topic:- sequence and series

Q: (D² - 2D + 1)y = 0; when x = 0, y = 1, Dy = - 1.

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Q: The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A…

A: Distance of satellite from station A and height of the satellite above the ground is

Q: Let K/L be ideal of quotient ring R/L. If K is prime ideal and contains L, then K/L is prime ideal.…

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Q: 3. y= (sec ³x + tan ²x)

A: Topic:- application of derivatives

Q: The area bounded by y = 2x² - x³, and y=0 is revolved about x=0. Find the volume of the solid…

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Q: Find the area of the surface obtained by revolving the graph of x = y³ on the interval [0,1] about…

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Q: The graph of y = f(x) is given. 5 4 1 -4-3-2-1 123 -1 324 2 2 -5 -6+ State the value of each limit,…

A: Consider

Q: 2 · S² f 0 Given f(x,y) = x²y-3xy³. Evaluate A-6y³ +8y/3 14y-27y3 B 6 6x² - 45x 4 D 2x² - 12x BARCE…

A: Given f(x,y) =x²y-3xy³ Now integration of 0 to 2 (x²y-3xy³)dx  = (X³y/3-3x²y³/2) limit 0 to 2 Put…

Q: Evaluate the integral. Do not use hyperbolic functions as the final answer. 1 -dx 2 √√3x²-4

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Q: Solve the given ODE using the method of undetermined coefficients. y" – 4y = (x² − 3)(sin2x)

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Q: 6. Find of z = In(xy) 8²y

A: Given:       z=lnxy     ∂z∂y=∂∂ylnxy  Treat x as constant  Apply chain rule:…

Q: Given f(x,y) = x²y-3xy³. Evaluate (A) 2x²-12x B (C) (D) -6y3+8y/3 14y-27y3 6 6x² - 45x 4 2 1 fdx

A: Topic = Integration

Q: Evaluate Jx/2 6 sin x (cos x + 1)³ dx

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Q: C Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that…

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Q: y" + y = secx tanx

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Q: If = (-12,4,8) the position vector of u is.............

A: We know that if a=<x,y,z> then its position vector is a=xi+yj+zk.

Q: 6-18x4 ic notation and fractions where needed. Give your answers in the form of comma separated li…

A: Topic:- calculus

Q: 4. Given z = *-y x+y Find az/ax

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Q: Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a…

A: We can solve the given question as below.

Q: 9. A gutter with trapezoidal cross section is to be made from a long sheet of tin that is 4√108…

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Q: Problem 2: Use the definition of the Laplace transform to find the transform of the piecewise…

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Q: Find the general solution of the following 2nd order differential equation: y* +2y + 2y = 0

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Q: da potential function f for the field F. F = (4y + 2z)i + (4x+z)j + (2x+y)k eneral expression for…

A: Topic:- application of integration

Q: Question 16 The area bounded by y=1-x²₁x+y=1 and the x-axis is submerged vertically in the water…

A: We need to choose correct option.

Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

Q: Find the point equidistant from the points (0, 0, 0), (0, 4, 0), (3, 0, 0), and (2,2, -3).

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