Verify Green's Theorem by evaluating both integrals aN dx + x² dy = / / dA ay y2 ax for the given path. C: boundary of the region lying between the graphs of y = x and y = Vx | y2 dx + x2 dy дм dA ду ax

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A: The given graph is distance against time ,  where distance is marked on y-axis and time marked in…

Q: 3. Compute f(x)dx 2х if x<1 f(x) = { 4 if x21

A: As we know from the property of the definite integral. ∫abfxdx=∫acfxdx+∫cbfxdx And The Power rule:…

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A: A detailed solution is given below

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A: Given can be written as (D2-D-6)y=2 The general solution will be y=CF+PI Complementary Factor(CF):…

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A:

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A:

Q: Find the directional derivative of the function

A:

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A:

Q: Find the arc length of the graph of r(t) eV2li +e¬V2lj+2tk, 0<t< v2 ln 9 NOTE: Enter the exact…

A: Given problem:-

Q: Find the following for the given equation. r(t) = 8 cos(t)i + 8 sin(t)j (a) r'(t) = (b) r"(t) = (c)…

A:

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A:

Q: Find r'(t) r(t) = 6Vti + t²V¢j + In(2 )k r'(t) =

A: Given r(t)=6ti+t2tj+ln(t2)kThat is…

Q: Determine f„ (0, T, 1), fy(0, , 1), f¿(0, r, 1) given the function z sin(3xz+ y²)

A: The given function,        zsin3xz+y2

Q: sin x – 2+ csc x (c) sin x – 1 sin x CSc x sin x + 1 | 1 (d) cos(tan-l x) = V1+ x² 1+cos u (e) Using…

A: We have to answer following Questions.

Q: x² + 4x + 1 dx (x – 1)(x + 1)(x + 3) d* - Inlx- 1+Inlx+11- n|r+ 3| +C Inlx- 11+Inlx+1| +Inx + 31 +C…

A: Let's find.

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5- 5 -5+ -5+

A: Given data÷

Q: Ex: Investigate the convergence of the following series. H.W 1 7 2) ΣΥ-1 3n 2n+5n IL !

A:

Q: æ = (f+ a)soɔ Which among the choices is equal to the dy/dx? In your sc - cos(r+y) A)

A: Given: cos(x+y)=x

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A:

Q: Find the first partial derivatives with respect to x, y, and z. 7xz x+y

A: This question is related to differentiation, We will solve it using given information.

Q: 5 x X LOS

A: Given: I=∫0πsin5x2cos7x2dx  ...1   As we know that; The Power rule: ∫xndx=xn+1n+1+C

Q: 3e dt 10. SET A.

A: We will use the concepts of definite integral

Q: Question 2 Find the inverse Laplace transform of H(s) - (;+)-

A: H(s)=1s2-e-s1s2+2s+e-4s4s3+1s L-1{H(s)}=L-11s2-e-s1s2+2s+e-4s4s3+1s…

Q: Evaluate the following sum: 3x + cos 2016 + cos (Write your answer in the simplest form, use…

A: The given sum,1+cosπ3+cos2π3+cos3π3+cos4π3+......+cos2016π3

Q: Fill In The Blank Refer to the given below. Find the indefinite integral. Simplify your final…

A:

Q: 2. Integrals containing sin u cos v can be solve using identity. (a) Double-angle (b) Half-angle (c)…

A: Let's find.

Q: 2. (Section 9.2) A refinery produces both gasoline and fuel oil, and sells the gasoline for $4.00…

A:

Q: 3. Differentiate. SET A. y = 3 cos(5x2 + 2)

A:

Q: Integral

A:

Q: Find V · (V × F) if F(x, y, z) = 7 sin xi + 10 cos(4x – 5y)j+ 5zk.

A:

Q: Find the first three non-zero terms of the Taylor expansion for the given function and given value…

A: The Taylor series;  fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+..... Where, center at x=a.   Given:…

Q: -(1/3), 3/9, -5/27, 7/81

A:

Q: 46n Nhich of the following angle measure (in radians) is coterminal to an angle with measure 3…

A: Given problem:- Which of the following angle measure 46π/3 (in radians) is coterminal to an angle…

Q: Approximate the point of intersection of the graphs of f and g. Then solve the equation f(x)=g(x)…

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

Q: Represent the plane curve by a vector-valued function. x2 + y2 = 36 r(t)

A:

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

A: Here we have r(t)=t2i+t5j We have to find κ(t)=r'(t)×r''(t)r'(t)3 ..................................…

Q: d Calculate r1(t) · r2(t)] and dt d [ri(t) × r2(t)] first by differentiating the product directly…

A: Given that,       r1(t)=9t i+4t2j+5t3k,   r2(t)=t4k

Q: What I Have Learned Let us now measure what you have learned in this module. Choose the letter of…

A:

Q: S(1 – 2x²)(x + 3)dx

A:

Q: 4. (x³ + 3x – 1) dx 2 5. 4x x2 6. SIy + 1) – (y? - 1)]dy

A:

Q: Which of the following is an antiderivative of f(x) = sin x cos x? %3D (a) sin²x (b) cos² ¤ sin 2x…

A: We can find the answer as below.

Q: 3. y = In? (csc2x). Find y"

A: y=ln2(csc2x)

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A:

Q: x2- 2 (x+ 2)(x + 1)² x+2 (x + 1)2 x+2 (I + x) Option 1 Option 2 1 (x + 1)2 x+ 2 (x + 1)

A:

Q: Find the sum of the following power series: 3 3.7 1+7** 4-8 3.7.11 3.7.11.15 + 4.8. 12 4.8. 12• 16…

A:

Q: Find the distance between the two parallel planes 5x – 3y + z – 2 = 0 %3D -10x + 6y – 2z + 3 = 0

A:

Q: Determine the amplitude, period, midline, and phase shifts of the function. Then write the equation…

A: Given problem:- Determine the amplitude, period, midline, and phase shifts of the function. Then…

Q: TIIS que IS mat you are usng your calc necuy. Use a calculator to do this calculation. 10-15 3.9 x…

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Q: on the interval Find the difference between the upper and lower estimates of the distance traveled…

A: Let's find.

Q: (b) Which of the following integrals is equal to –2+ ln 2? (a) 4 dx 4 (b) dx x² (c) / 4x dx x2 4 dx…

A: