Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 s t < 1. dy

Q: Find the area of the surface generated by revolving the curve y = /2x – x2, from x = 0.25 to x =1.7

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Q: Given y = (x + 1)(x + 2)² Find: y O (z + 2)(3x – 4) O (2 – x)(3x – 4) - O (x – 2)(3x + 4) O (2 +…

A: Apply the product rule of differentiation f·g'=f'·g+f·g' to find the derivative of the given…

Q: ne graph of f(x) = (2x + 1)- %3|

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Q: Which equation represents the graph shown below? 350 300 250 200 150 100 50 -40 40 80 120 160 200…

A: The given graph is of sin x.

Q: 16. What is the derivative of f(x) = eBx+3? a. f'(x) = e® b. f'(x) = 3e®x c. f'(x) = 8e d. f'(x) =…

A: 16. fx=e8x+317. y=34x18. fx=x3-3x2-3

Q: Find the minimum amount of tin sheet that can be made into a closed cylinder having a volume of 108…

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Q: Match the vector field with its graph. F(x, y) = yi -6+ 世 -5+

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Q: 5 8. Let f(x) =-x + 4 cos 3x. On the interval 0 < x< 2n, what is the average height of the function?…

A: A detailed solution is given below

Q: (2x – 3y) dx + (2y – 3x) dy

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Q: What is the third derivative of the function: f(x) = x5 - 4x³ + 3x?? O 5x – 12x² + 6x O 20x? 24x + 6…

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Q: 9.) A particle moves in a straight line according to the law of motion: s=cos(x). a. Find the…

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Q: Show that the differential form in the integral below is exact. Then evaluate the integral. (-2,4, -…

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Q: Find the first three nonzero terms in Maclaurin Series for each function

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Q: Consider the following functions. f(x) 3 Vx - 3 g(x) = x – 3 %3D Sketch the region bounded by the…

A: Let us first find the intersecting point. So,               x-33=x-3⇒x-3=x3-9x2+27x-27⇒x=2, x=3, x=4…

Q: Find curl (3z i + 4x j + 7y k). curl(3z i + 4x j + 7y k) = i Di + ( Dj + ( i )k

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Q: 2 4 Find an equation of the normal line to the curve 3x¯y' – x°cos(ny) + 4x + 2 = 0 at the point…

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Q: Find the derivative of the function f(x) = – 2x1 + 5x – 7. A. -2x + 5 C. -2x? + 5 E. None of these…

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Q: Consider the function f(x) = 12x° + 30x4 – 300x³ +3. f(x) has inflection points at (reading from…

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Q: Evaluate: Lī 3sin13 xda 512 1001 1024 1001 1024 1001 512 1001

A: Solved below.

Q: Find div F and curl F if F(x,y, z) = x°i – 5j + yzk. - div F= curl F=

A: A detailed solution is given below

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

A: The objective of the question is evaluate the definite integral and choose the correct option . Here…

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 550…

A: We have to find the minimum cost.

Q: Find V (F x G), if F(x, y, z) = 11xi +j+ 13yk and G(x, y, z) = xi + yj – zk. V. (F x G) =

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Q: Find div F and curl F if F(x, y, z) = 3y°z°i – 3x*2°j – 3xy*k. - div F= curl F=

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Q: Evaluate the integral / (2x + 9y)dx + (6x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

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Q: Find the derivative of the function f(x) = 4v3x² – x. 12х - 2 A. V3x2-1 6х - 2 бх — 1 C. V3x2 –1 E.…

A: To find the derivative of f(x)=43x2-x

Q: Find curl (4z i+ 5x j+ 8y k). curl(4z i+ 5x j+ 8y k) = ( )i +( i j+( i )k

A: To Find : curl(4z i + 5x j +8y k)   Note that : If F=〈P,Q,R〉 is a vector field in ℝ3, and Px,Qy, and…

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: Here,  a→(t)=3t i^+6 sin(t)j^+cos(2t)k^⇒v→(t)=∫3t i^+6 sin(t)j^+cos(2t)k^dt⇒v→(t)=3t22 i^+6…

Q: Given the function g(x) = 8x³ + 12x² – 48x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

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Q: Evaluate et-2 lim x→2 _x – 2 1 O +∞ O 1 O -00

A: Use l hospital rule for finding the correct option.

Q: If a rock is dropped from a height of 193 ft, its poistiont seconds after it is dropped until it…

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Q: Evaluate the integral (2x +3y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: Find div F and curl F if F(x, y, z) = 7e*" i - 10 cos yj+ 8 sin² z k. div F=| curl F=

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Q: (5x2 – y²) dx + 2ydy = 0

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Q: esin(a

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Q: Find the first three nonzero terms in Maclaurin Series for each function

A: This is a problem related to series expansion. based on the general formula of maclaurin series we…

Q: Evaluate the line integral / (4x + 8y)d.x + (4x – 9y)dy along the curve C : x = 10 cos t, y = 20…

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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)…

A: This is a problem related to derivative of the function. For calculating the unit if derivative…

Q: Solve the initial value problemy-10y +50v-0 for y(0)-1 andy (0)-5. After getting the equation for…

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Q: Verify Green's Theorem by evaluating both integrals aM y? dx + x² dy = | / (G dA ay əx for the given…

A: Solved below.

Q: A man has $380,000 invested in three rental properties. One property earns 7.5% per year on the…

A: Given problem:- A man has $380,000 invested in three rental properties. One property earns 7.5% per…

Q: Verify Green's Theorem by evaluating both integrals Lr dx + x* dy = / dA ду x² dy ax for the given…

A: In this question we verify Green's Theorem                 i.e, verify integral  ∫C y2 dx +x2 dy =…

Q: ntinuous function, f (x), has a domain of [-6, 6] -6 <x<-2 x=-2 -2 <x< 0 x=0 0 < x<6 does not exist…

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Q: (c) Show that the differential equation ry" – 3y + zy = 0 has a general solution of the form y(z) =…

A: given that differential equation   xy'' - 3y' + xy = 0…

Q: The fifth derivative of the function f(x) = 5x° is a constar False O True

A: Given query is to find statement is true or false.

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: | x(x + 10)" dx

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Q: Evaluate the triple iterated integral. xyz³ dx dy dz

A: ∫02∫02∫-14xyz3dxdydz=∫02∫02x2yz32x=-1x=4dydz…

Q: What is the area bounded by the graph of r 3-2sin0? O A = 2 (3 – 2sind)² d® O A = 4 5 (3 – 2sin8))°…

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Q: Evaluate the following limit: lim x→2+ x – 2 O No answer text provided. |- 1/2

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