Verify Green's Theorem by evaluating both integrals ƏN dA y? dx + x² dy = ay for the given path. C: boundary of the region lying between the graphs of y = x and y = x2 | y? dx + x2 dy = ON dA = ax ду

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A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

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Q: Given the vectors A = 3i – 5j + 2k and B = 7i + j – 2k. Find the vector projection of A onto B.

A: Given : A→=3i-5j+2kB→=7i+j-2k     To Find : Vctor Projection of A→  onto B→

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Q: 5.) Matching : Match the terms at the right with the best term on the left that matches it. Secant…

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Q: ||r'(t) × r"(t)|| ||r(t)||³ Use the formula k(t) to find k(t). r(t) = 2 cos(4t)i+ 2 sin(4t)j + 9tk…

A: We have to solve k(t)

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A: Given that       r = 10 cost i + 8 sint j - k

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 4…

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Q: xe 1. lim, »o X→0 1-e*

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Q: Find V · (V × F) if F(x, y, z) = 10 sin xi + 7 cos(9x – 10y)j + 3zk. V·(V × F)

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Q: ||r(t) x r"(t)|| Use the formula k(t) to find k(t). r(t) = 8 cos(8t)i + 8 sin(8t)j + 5tk к(€)

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Q: 6) y' = 2x-3y+4 x+y+2

A: Differential equation

Q: Use the graph of the function f(x) shown below to evaluate lim f(x). x 3+ 3 2 3 O 3 O 1 O DNE 2.

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 4 1 lim t→+∞ \ 3t2 +4' 2t (13, 0)

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Q: Consider the function f (x, y)=-2x'+3x'y+2 y°-9y+5

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Q: FIND THE INTEGRAL OF YOUR ANSWERS IN 2a and 2b  Note: My answer on 2a and 2b will be found on the…

A: This is a problem related to integral of the function. Based on the general formula we will answer…

Q: What is the differential equation whose solution represents the family y = Ae3x + Be 3x+Ce4x? %3D O…

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Q: Given f(x) = 3x2 – 24x + 15, a. Write f(x) in standard form. b. What is the axis of symmetry of…

A: Given query is to write the standard form and find symmetry.

Q: Determine whether the improper integral diverges or converges. In x dx O converges O diverges…

A: Use integral test for checking the convergence of series

Q: -6 Evaluate , (2x + V) dx. A. 27 + 2/3 + 4/6 B. 27 2/3 C. 27 23 4V6 D. 27 + 4v6

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Q: se Hooke's Law to determine the work done by the variable force in the spring problem. A force of 9…

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Q: Determine whether each of the following functions is (a) continuous (b) differentiable 5. f(x) = 2x²…

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Q: What is the volume of the solid formed by revolving the region bounded by the graphs of x2 = 5y and…

A: To find the integral of volume of solid formed by revolving the given region.

Q: Evaluate -5x lim,→0 tan x O -5 O 1 O 5

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Q: What is the equation of the plane that is tangent to the graph of z = x coS y – ye“, when (x, y) =…

A: Equation of the plane tangent to the surface z=f(x,y) :               Let   F(x,y,z) =0 ,then…

Q: (1-) 3 4. lim

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Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

Q: 7.) Evaluate the following definite and indefinite integrals a.) ò (5-2x* -2x*-cos.x)dx +6x)dx b.)

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Q: If the function f(x) is continuous in the interval [2,8] and f(2)=-7 and f(8) = 9, %3D then which of…

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Q: _13. If y = sin(4x – 5), then what is y'? а. у'3 сos (4x -5) b. у'- 4cos (4x — 5) c. y' = -cos (4x -…

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Q: The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the…

A: Given: r→t = 310t-sin10ti→+31-costj→ We know the following rt  =…

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

A: Here we have to use green's theorem.

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

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Q: Consider the function f(x) = 2 – 7x², - 4 <x < 2. The absolute maximum value is and this occurs at x…

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Q: Evaluate the definite integral. Using Fundamental Theorems of Calculus. π 1 sin -x cos? 1

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Q: Evaluate the following limits. If needed, enter INF for oo and MINF for -oo. (a) lim (Va + 3r +1-1)=…

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y°x²j+ 5z'yk. ,62 div F= curl F=

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Q: Consider the function f(x) = 9x + 4x-1. For this function there are four important intervals: (- 00,…

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Q: Find div F and curl F if F(x, y, z) = 3y°z©i – 3x*z°j – 3xy*k. div F= curl F=

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Q: Find the first four nonzero terms in the Maclaurin series for f(x). f(x) = e 5x sin x ... Choose the…

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Q: Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

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Q: Find V· (F x G), if F(x, y, z) = 10xi +j+7yk and G(x, y, z) = xi+ yj – zk. V · (F × G) =

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Q: Find the area between the loops of the limacon r= 7(1+2 cos 0). Area =

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Q: dx 3-x

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