Use the Fundamental Theorem of Calculus to find the "area under the curve" of f(x) = 8x + 7 %3D between z = 8 and z = 10. Answer:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 3…

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Q: Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) (x² + lim x + 5…

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Q: Find the general solution of the equation. Express the solution explicitly as a function of the…

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Q: Find an equation of the tangent plane to R(u, v) = (e" sin u , eº cos u , e¯-" ) at the point where…

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Q: Find V (V x F), if F(r, y, z) = 7e""i + 2xe"j- 3e""k.

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Q: dy onsider the differential equation dx y? ) Re-write the equation in terms of differentials: dy =…

A: Given query is to find the solution of the differential equation.

Q: coso de by trigonometric substitution.

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Q: 2. By differentiation rules , evaluate the derivatives of the following and simplify as possible:…

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Q: (x^2+y^2-3)dx-2xydy=0 Prove the given DE is exact, and find general solution

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Q: Use Newton's method to approximate the indicated root of the equation correct to six decimal place…

A: Here, let the given function be: f(x)=x2+ex-9⇒f'(x)=2x+ex Next,…

Q: lim 2?e --00 1- cos(2x) im

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Q: Find div F and curl F if F(x, y, z) = 12y"2³i – 3x"z+j – 4xy°k. div F= curl F=

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Q: In |V Vr+i-2 dt, if we let / Vr+1 - 2, then dt is equal to A 4x°dx None 2(x²+ 2)dx (4x³ + 2)dx E…

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Q: V10x – 7y – 10 Find lim by rewriting the fraction first. 10x - 7y – 100 (x,y)→(10,0) 10x - 7y + 100

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Q: ermine the Interval(s) for which the function is (a) increasing, (b) decreasing, and (c) constant.…

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Q: A point Q moves along the intersection of the sphere a? + y? + 2² = 1 with the 2. At what rate is z…

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Q: Describe the graph of the equation. r = 12 sin 6t i – 12 cos 6t j O Itis a circle of radius 6 in the…

A: To find: Discribe the graph of the equation

Q: Describe the graph of the equation. r = (5 – 31) i – 1ltj O Itis a line in 2-space that goes through…

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Q: Determine the vector field of F. F(r, y) = yi – xj

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Q: (x) = V19+r dt , find f'(3)

A: Given query is to find indicated derivative.

Q: 4. Consider the figure below. y=4 x Find the volume of the solid generated when the shaded area a.…

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Q: Let f(x) be the function 2a² – 4x + 11, Then the quotient f(2 + h) – f(2) - can be simplified to ah…

A: The equation of line between two points;(4, -3) and (-3, 0)f'(4)=0+3-3-4=-37passes through (-3,…

Q: Solve the differential equation for general solution dy = - dx V y = 14x + C O y = /14x + C, or y =…

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: Solution: C′(x)=3x2 −5x​; C(0)=2,000

Q: V = f(x, y) = x²y ,x(t) = 2.

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Q: lim In(z – 1) – In(x“ – 1) = %3D

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Q: dy = 2 – y dx Find the correct direction field for the differential equation ノー\\ ババーと

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Q: S Sec ta

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Q: Find the work done by F in moving a particle once counterclockwise around the given curve. F= (x-…

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Q: .1//7 7 arccos x x² dx V1- x 1 –

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Q: 6. (ax3+ bx2+cx) dx= 2b | x2dx where a,b and c are constants. -9 A) True B False

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Q: If f(x) cos-(2x+5) 2, then dom(f) = %3D a+3 (A) (–3, –2) (B) [-3, –2] (С) (-3, —2] (D) (–1,1) (E)…

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Q: x + 4 1. Evaluate dx. Vr2 + 8.x

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Q: Given / f(x)dx = -3 and / g(x)dx = 6 , evaluate (a) / ise) – 59(=)|dz 1 *(x) + (e) [ 15(4) – o(=) +…

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Q: f (x) = x² + 1

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Q: Find V· (V × F) if F(x, y, z) = 4 sin ci + 7 cos(9x – 10y)j + 10zk. V · (V × F) =

A: Given F(x,y,z)=4sinx i+7cos(9x-10y) j+10z kTo find∇·(∇×F) first we need to find ∇×Fwe know that ∇×F…

Q: The circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm. Use inear…

A: Given problems:- 1).    The circumference of a sphere was measured to be 76 cm with a possible error…

Q: (b) Using the Power Rule for differentiation, find the derivatives for the following functions: (i)…

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Q: dx (r-1)%

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Q: Solve the problem. Solve the differential equation model of a population growth: dP 0.5P. dt O P(t)…

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Q: 23 + 7x + 9 Find dy: y = 1² + 4 dy :

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Q: Evaluate the integral directly by integration with respect to x and y. 4 x= (y/4)+ 1 4x - y -dxdy 4…

A: We have to find the value of the double integral ∫04∫x=y4x=y4+14x-y4dxdy Since dx present first in…

Q: as (x*ty3) dx -2メydy =0 a.) prove if the given DE is exact or non -exact - Given DE b.) Find its…

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Q: Given a function f(x, y) = e"y². (a) Find the gradient of f. (b) Evaluate the gradient at the point…

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Q: Find V (V × F), if F(r, y, z) = 7e"i+6xe"j – 2ev²k. V· (V × F) =|0

A: We have to find ∇.∇×F→

Q: In 1 decimal place Find the Surface Area generated by rotating the first quadrant portion of the…

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Q: Find V. (F x G), if F(x, y, z) = 10ci +j+13yk and G(x, y, z) = xi + yj – zk. V. (F × G) :

A: To solve the following problem

Q: ||r(t) × r"(t)|| ||r"(t)||* Use the formula k(t) to find k(t). 13 r(t) = 3 cos(3t)i+3 sin(3t)j + tk…

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Q: Find the third degree Taylor polynomial centered at 2 for the function f(x)=e²* + 3.x .

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Q: If {(=)dz = f(x)dx f(x)dx + f(x)da f(x)dx, what are the bounds of integration for the first…

A: Solution: