Find a such that the line x = a divides the region bounded by the graphs of the equations into two regions of equal area. (Round your answer to two decimal places.) y2 - 16 – X, X = 0 a =

Q: Calculate x sin(y)dxdy

A: On solving this we will get

Q: Evaluate the line integral-ydx + xdy along the curve C: y? = 21x from (21, 21) to (0,0). NOTE: Enter…

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Q: E. Find the point of intersection of the plane 2x+3y+z 5 and the line x- 3 y+4 z- 1 1 II

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Q: Evaluate JJ xy dA , where R is the region in ху ´(1, 3) (5, 3) R (2, 1) (4, 1) A) 56 в) 67 38 D) 90

A: I am going to solve the problem by using some simple calculus to get the required result of the…

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Q: Express the iterated integral as an equivalent integral with the order of integration reversed. 30…

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Q: Evaluate the following integral: |sec2 (z) tan (z) dz = 因团 +C Be sure to enter powers of…

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Q: 31.| CSC I COLI dt

A: We will use substitution method to solve both the integral.

Q: af Find for the function: f(x, y) = xcos(xy) + 2xy2

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Q: -6w + x + 3y + 6z = -6 -7w - x – 9y – 2z = -33 -4w – 9x + 8y + 9z = -94 -w – 6x – 10y + 9z = -202…

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Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: Vector equation of a line passing through P(a,b,c), Q(p,q,r) is given by,…

Q: Evaluate the integral. (Use C for the constant of integration.) 2 cos (a) da sin(a)

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

Q: Calculate the area of the region bounded by the graphs of the given equations. x 2y2- 4, x = y2 + 5…

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Q: Evaluate the integral. NOTE: Enter the exact answer. xe* dy dr =

A: the integration of the double integral is xexy.

Q: Use a double integral to find the volume under the plane z = 22x + yand over the rectangle R = {(x,…

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Q: Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the…

A: We need to set up and evaluate integral.

Q: 16. Find the volume of the region that lies under the graph of the paraboloid z = over the rectangle…

A: Here, to find the volume of the paraboloid z=x2+y2+2 over the rectangle R=(x,y)∈ℝ2|-1≤x≤2, 0≤y≤2

Q: Apply the Ratio Test to each series to determine whether the series converges, or state that the…

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Q: Find V x (V × F) if F(x, y, z) = 4.xyj+2xyz k. ▼ × (V × F) = %3D

A: ∇×F=i^j^k^∂∂x∂∂y∂∂zPQR  for a vector F=Pi+Qj+Rk in terms of x,y,z

Q: Given h(r) = 1/r+3 find the following: (a)h(x2)= (b) h(x2 + 1)= (c)h(x2) + 1=

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Q: moving in the xy-plane. Position Vector Point r(t) = 6 cos ti + 6 sin tj (3/2, 3V2) (a) Find the…

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Q: Evaluate the integral by choosing a convenient order of integration: x cos(xy) cos' (Tx) dA; R 0, x…

A: Given

Q: 10 Find div F and curl F if F(x, y, z) = xz°i+ 5y"x²j+ 4z?yk. div F= curl F=

A: Solution:

Q: n/2 c sine Evaluate the iterated integrals J. r cos e dr de 0. A 1/6 B 1/2 c) 6 D) 11/9

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Q: Find the volume of the region enclosed by z = 1 – y? and z = y² – 1 for 0 < x < 21. V =

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Q: Determine the area of the region enclosed by y=x^2 and y=x^1/2

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Q: 13. Calculate the divergence of the vector field F = x1e1 + 2x1e2 + +nx1en. ...

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Q: Fidn the sum: 2k (Write your final answer in fraction form, when applicable) A=31

A: Use the formula of summation then put the limits .

Q: The velocity of a car is v(t) = 42(t - 2)(t - 4) miles per hour on the time interval [0, 4] hours.…

A: We need to find distance traveled by car.

Q: Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 А) 6 B) 9 12 15

A: Let's find.

Q: Recall the geometric series 1/(1 − x) = 1 + x + x^2 + x^3 + x^4 + . . . for |x| < 1. Determine the…

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Q: Evaluate the line integral (6x + 8y)dx + (3x – 3y)dy along the curve C: x = 4 cos t, y = 8 sint…

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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 24x from (24, 24) to (0,0). NOTE:…

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Q: Find div F and curl F if F(x, y, z) = 7e*i – 6 cos yj+ 6 sin? z k. div F= curl F=

A: DivF  and curl F are evaluated.

Q: Use Ore's theorem to prove that any n-vertex graph G for which |E(G)|> (",') +2 is Hamiltonian.

A: answer is in next step

Q: Calculate y" (x) and y" (x). бх — 6 y(x) (Use symbolic notation and fractions where needed.) y"(x) =…

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Q: Evaluate the iterated integral. x dz dy dx 128/15 16/89 23/6 6.

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Q: Use the gradient to find the directional derivetive of the function at Pin the drecton of v n(x, y)…

A: Directional derivative of a function f(x,y) at a point P(a,b) in the direction of the vector v=ai+bj…

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 7 cos(t)i…

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Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) =…

A: The given function is: f(x)=e-5x

Q: Let y = (3x + 2 sin(x))*. Find f(x) and g(x) so that y = f(g(x)) and compute the derivative using…

A: Here the given function is: y=(3x+2sin(x))4

Q: Зху dx + 4xy dy %3D i 63

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Q: -Ive the derivative dy for the function: x dx = e'sint ; y = ecost %3D

A: To find dy/dx.

Q: Find the area of the region using a double integral. The region bounded by y = 4x°, 2x + y = 6, and…

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Q: Find div F and curl F if F(x, y, z) = x'i – 3j + yzk. div F= curl F=

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Q: Find curl (5z i + 6x j + 3y k). curl (5z i + 6x j + 3y k) = ( i )i + ( i i )k

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Q: 2. Find the area of the parallelogram whose vertices are given by: P: (1,2, –1), P2 = (4, 2, -3), P3…

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Q: Find ▽ x (▽xF) if F(x, y, z)=10xy j+ 10ryz k.

A: The value of ▽ x (▽xF) is (10 + 10y)i + 10xj + 0k

Q: 7. Determine the following general antiderivatives. cos (x) dx -dx sin(x) а. - b. 10 sin(x)cos(x) dx…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: For each of the following series determine if the series converges or diverges. 00 In(n) Σ n n=2 n3…

A: The given series,1. ∑n=2∞ln(n)n2. ∑n=0∞n3n4+1