Determine the area of the region bounded by y=2x^2+10 and y = 4x+16

Q: R be the region bounded by the curves y = 10 − x^2 and y = x^2 − 8x. Set up, but do not evaluate,…

A: Given query is to setup the integral for area .

Q: Find curl (9z i + 10x j+ 7y k). curl (9z i+ 10x j + 7y k) = ( i Di + ( i Oj + ( i )k

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Q: he curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i + 4 sin(t)j + tk; t 2…

A: Please refer to the image below

Q: The graphs of the function f (r) = 7 - a and g(a) = 3 are given below. %3D

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Q: Find V x (V × F) if F(x, y, z) = 8xyj+7xyz k. V × (V × F) =

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Q: Find div F and curl F if F(x, y, z) = x°i – 2j + yzk. div F= curl F=

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Q: A spring has a natural length of 22in. A force of 16001b stretches the spring to 32 in. How far…

A: We will use rules of spring stretch to solve it.

Q: Find the approximate area under the curve of f (x) =cos (5) from x = 0 to x = TT, using 4…

A: Here, the interval [0,π] is divided into 4 intervals of the length of each interval is ∆x=π-04=π4.…

Q: 12. Find an equation for the tangent plane to the surface given by 2xy? = 2z2 – ryz at the point (2,…

A: We know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Where n→-nxi+nyj+nzk is…

Q: nd the S (1–) dx A. x– 2 In|x| – +c B. 3x – 2 In|x| –-÷+c C. 2x – In|x| –+c D. x– In|x| - +c

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: xe*y dy dx

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Q: 4 fy 1 -3 -2 1 -1 -2

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Q: Use the graph of the function f to decide whether the value of the given quantity exists. (If an…

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

Q: 1. E(n + -3 2 n=1

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Q: (b) trte) × u(t)] dt (i) Find the product first, then differentiate. (ii) Apply the properties of…

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Q: A tank originally contains 100 gal of fresh water. Then water containing - Ib of salt per gallon is…

A: Given , A tank originally contains 100 gal of fresh water. Then water containing (1/2) lb of salt…

Q: Find div F and curl F if F(x,y, z) = x*i – 7j + yzk. - div F= curl F=

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Q: Evaluate the line integral / (3x + 9y)dx + (4x – 5y)dy along the curve C : x = 10 cos t, y = 20 sin…

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = t'i+ t3j K(t) =

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Q: dy Solve the derivative dx for the function: x = e'sint ; y = etcost

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Q: (1 point) Use the Divergence Theorem to calculate the flux of the vector fields F, = -Szi + 5xk and…

A: Find your answer below

Q: Find these derivatives

A: Our Aim is to find the derivative of the following functions given below:-(i) y=e2x cos (x)(ii) y=ln…

Q: Find the unit tangent vector to the curve at t r(t) = t°i + 3t?j, t= 2 T(2) =

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Q: Evaluate the indefinite integral: .3 dx x² – 2x + 5

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Q: Using the substitution u = sin (x), or otherwise, find the exact value of %3D J sin° (x) cos (x) dx.…

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (ei + Sin(/2)j + e stk…

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Q: Find the e v

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Q: 1. Use the midpoint rule with n = 6 to estimate the value of the integral (x + x)dx. (5 points) 2.…

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Q: Find div F and curl F if F(x, y, z) = 3e*"i – cos yj+ 7sin? z k. %3D div F= curl F=

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Q: ||r'(t) x r"(t)|| Use the formula k(t) : to find k(t). 3 r(t) = ei+etj K(t)

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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: (6x- y+3)dx+(3y'-x-2)dy 6) Integration Factor Method rahee

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Q: Calculate D(fog) for the functions f(x, y, z) (st, tu, su).

A: answer is in next step

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 area of the surface that is generated by revolving the portion of the curve y= x² between x…

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Q: Find div F and curl F if F(x, Y, z) = xz°i+ 2y°x²j+ 2z²yk. 6 div F= curl F =

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Q: Find the limits of integration ly, uy, Ix, ux, Iz, uz (some of which will involve variables a, y, z)…

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

Q: Find the principal unit normal vectóř tô thể curve at the r(t) = /2ti + e'j + e-k, t = 0 %3D

A: Principal unit normal vector

Q: H.W (5) Solve the following differential equations of (3x -6xy)dx+(-3x' -2y)dy 0

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: Directional derivative: D f = del f • unit vector of direction

Q: dx 1-e-* Evaluate A. 2ln|e* – 1|+ c B. Inle* – 1|+x +c C. 2 In|e* – 1| +x+c D. Inle* – 1|+ c

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Q: Evaluate the iterated integral. IT (10 + 2x2 + oy?) dx dy

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Q: Use the Comparison or the Limit Comparison test to show convergence or divergence of each series.

A: Explained below

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: If 0 =. then sec(8) =1 (Write your answer in the simplest form, use fractions whenever applicable

A: Explanation of the answer is as follows

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: Sketch a single graph of a function f(x) which satisfies all of the following the limits and values.…

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Q: find area OPShaded Pegion ニ 16x

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Q: Find the approximate area under the curve of (X) = x²+1 from x = 0 to x = 2, using 4 left- endpoint…

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Q: Find the S(x* +) dx xe-1 А. 1x? + c e-1 4e xe+1 В. Ix2 + c e+1 2e xe+1 С. 1x3 + c e-1 Зе xe+1 1 D.…

A: Given query is to find the derivative of the expression.