4. Under the usual addition 47Z/2021Z .

Q: 4 y=V4x- 2/2x

A: Topic = Derivative

Q: Find the curvature and the radius of curvature at the stated point. r(t) 2 cos(t)i+ 3 sin(t)j+ 10tk;…

A: Solving

Q: Find V· (V × F), if F(x, y, z) = e*²i+3xe'j – 7e*k. V . (V × F) = x z evz 三

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Q: 1. dt 15. y= 17. y 0 tan 0 d0

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Q: What is the closed-form expression for the series 2 (k+ 1)², k=1 13 n3 + B

A: First expand the squre  term and make it in standard format then use the formula of summation.

Q: Question 7 Find the area of the region(s) enclosed by the curve f(x) = x³, the x-axis, and the lines…

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Q: The integrand of the definite integral is a difference of two functions. Sketch the graph of each…

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Q: Find the centroid of the region. NOTE: Enter the exact answers. (ï, §) = (?, ?) y = r

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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: Find curl (9z i + 10x j + 5y k). curl (9z i + 10x j + 5y k) = ( i )i + ( i j + ( i

A: Curl

Q: Consider the contour represented in the following figure. The points marked on the figure are A(5,…

A: Dear learner, As per our guidelines we can provide the solution for first one only. Kindly post…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A:

Q: Consider the following. f(x) = x* – 4x² g(x) = x² - 4 (a) Use a graphing utility to graph the region…

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Q: Find r(t) for the given conditions. r"(t) = -4 cos(t)j – 3 sin(t)k, r'(0) = 3k, r(0) = 4j %3D %3D…

A: Given

Q: Question 9 1 2 1 Evaluate the iterated integral. J, J. J. (x²+ y2 + z?) dx dy dz -1°0 0, А) 5 В) з 8…

A: The solution is given in the next step.

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

A: Given

Q: Find the unit tangent vector to the curve at the specified value of the parameten r(t) = 4 cos(t)i +…

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Q: Sketch the region enclosed by the curves and find its area. cos 5x, y = 0, x = x = 10' 5 NOTE: Enter…

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

Q: Find the area of the region that is enclosed by the cardiod r = 14+ 14 sin 0. NOTE: Enter the exact…

A:

Q: In sketching the graph of y=f(x) = 2sin -5, we translate the graph of y=2sin by 5 units downward and…

A: To translate the given function.

Q: solution

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

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Q: d Find [r(t) · u(t)] and [r(t) x u(t)] in two different way dt dt r(t) = cos ti + sin tj + tk, u(t)…

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Q: The Taylor series for cos(x) centered at a = 0 is given by: (-1)",2n (2n)! n=0 Using this result,…

A: Given problem:-

Q: d d Calculate ri(t) · r2(t)] and [ri(t) x r2(t)] first by differentiating dt dt the product directly…

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Q: Find the area of the region inside the circle r = 12 sin 0 and outside the cardioid r = 4+4 sin 0.…

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Q: Use Green's Theorem to evaluate the line integral. y² dx + xy C: boundary of the region lying…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. V64-22 xy dy dx dz

A: Given: I=∫08∫064-z2∫0xxydydxdz   The Power rule: ∫xndx=xn+1n+1+C

Q: Find the area of the region(s) enclosed by the curve f(x) = x°, the x-axis, and the lines x =-1 and…

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Q: Find [r(t) u(t)] and [r(t) × u(t)] in two different ways. dt dt r(t) = cos ti + sin tj + tk, u(t) j+…

A:

Q: Question 14 1. 2 Evaluate the iterated integral. J, J. J. (x²+ y² + z?) dx dy dz -1°0 (А) 5 (в) з D)…

A: To find following integral valueI=∫-11∫02∫01(x2+y2+z2)dx.dy.dz

Q: A lunar module weighs 12 metric tons on the surface of the Earth. How much work is done in…

A: Given that: The weight of the lunar module on surface of the earth, We=12 metric-tons The height to…

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

A: Given

Q: Compute f(x)dx 2x if x 1 f(x)

A: To find out the integration.

Q: The graph of y=- 50co has a horizontal shift of A units with respect to the graph of y= - 50cos(x).

A: This question is related to Trigonometric functions, we will solve it using given information.

Q: r = V cos 20 r = 5 cos 0

A:

Q: Sketch the region enclosed by the curves and find its area. у %3 сos 9x, y —D 0, х - x = 18' 9 NOTE:…

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Q: Find the Laplace transform of f(t) ={0, 0 ≤t ≤1         7t −7, t ≥1 .}

A: Given :f(t)=00≤t≤17t-7t≥1

Q: Evaluate the integral. NOTE: Enter the exact answer. c10 1 xe"y dy dx

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Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

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Q: Use the Product and Quotient Rules as necessary to find the derivative of f(x) = 7x? cos(x) (Use…

A: The given function,      fx=7x2cosx

Q: Find the volume of the solid bounded by the plane 7x + 3y + 8z = 3 in the first octant. Leave your…

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Q: Find the area of the region enclosed by the curves y = x² and y 4.x by integrating with respect to…

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Q: first octant 2 4- x+y dy dx -

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Q: Evaluate the definite integral. 9ti + 3t°j + Vtk) dt

A: The given definite integral,    ∫-119t i+3t3j+t3kdt

Q: Find the volume of the solid generated by revolving about the y- axis the region bounded by the…

A: Given problem:- Find the volume of the solid generated by revolving about the y- axis the region…

Q: r2 cose dr de valuate the iterated integrals A) 1

A: ∫0π∫01-sinθr2cosθdrdθ

Q: xe*y dy dx

A:

Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere x² + y?…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 6…

A: A detailed solution is given below.