Solve the following: 1. Evaluate ſ x=dx 2. Evaluate S 4 dx 3. Evaluate S (x²+ x³)dx 4. Evaluate S Vx (x – 4)dx

Q: Evaluate the definite integral. NOTE: Enter the exact answer. 8j i2 + 3

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Q: 3+ x2 ' Find the vertices of the rectangle with maximum area. Vertices = Enter your answers as a…

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Q: What is the differential equation whose solution represents the family y = Ae3x + Be4x+Cxe4x? O…

A: Given problem:- Find the differential equation whose solution represents the family y=Ae3x +Be-4x…

Q: Verify Green's Theorem by evaluating both integrals y? dx + x² dy Ne dA ду ax for the given path. C:…

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Q: Do as indicated showing the details of your work. Show your complete se space provided and write…

A: We need to solve integral.

Q: 1) Find and of the following equation then simplify whenever possible. dx x = 2u* – u3 + u – 11 , y…

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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: Use logarithmic differentiation to find

A: answer is in next step

Q: What is the equation of the tangent plane normal to x2 + y2 + z = 9 at the point (1, 2, 4)? O 2x -…

A: Given; f(x,y,z)=x^2+y^2+z-9  Point (1,2,4)

Q: f(x) = (-3x³ + 4) 7, which of the following is f'(x)? f' (x) = 63x² (-3x° + 4)-8 - f' (x) = 63x(-3x…

A: Topic:- derivatives    Using  Derivatives of x^n = nx^(n-1)

Q: 1) Find and of the following equation then simplify whenever possible. dx x = 2u* – u3 + u – 11 , y…

A: Given: x=2u4-u3+u-11, y=5u3-4u2-7u+2     As we know that; The Power rule; ddxxn=nxn-1 The Quotient…

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

A: Differential equation

Q: d'y Find dx? 2 y = (2а-3)? dy 48 dx? (2г - 3)" O dy -12 da? (2г- 3)" O d'y 12 dx? (2a-3) dy -8 da?…

A: y=2(2x-3)2

Q: Describe the graph of the equation. r = (7 – 21) i + 10r j | O It is a line in 2-space through the…

A: The given equation is: r(x,y)=(7-2t)i+10tj⇒x=7-2t    y=0+10t

Q: | (2x - y) dx + (x + 7y) dy. Evaluate C: x-axis from (0, 0) to (0, -7) and (0, -7) to (4, -7)

A: x-axis from 0,0 to 0,-7 indicates that interval of y is from 0 to -7 y-axis from 0,-7 to 4,-7…

Q: (4) Evaluate each of the following indefinite integrals. r+2 (a) r² + 2r + 1 -dr (b) cos(2r) cos(r)…

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Q: О а. 1.56 J ОЬ. 3.25 J Ос. 1.94 J O d. 2.33 J

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Q: Laplace transform of (t+2)^2

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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: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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

A: Given: I=∫Cx+3y2dy And x=4t, y=8t  and 0≤t≤1   As we know that; The Power rule: ∫xndx=xn+1n+1+C

Q: Find y': y = /5+ 2x – x² - 1-x O y = V5+2x-a2 1 O y = 2/5+2x-a2 7-2x O y = 2/5+2x-a²2 O y = /2 – 2x

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Q: Evaluate lim, (-5x + 5 – 5 - ) 12 O + O 5 O-5

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Q: Solve

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Q: II. Use the first fundamental theorem of calculus to find F'(x) .Write your final answer on the box.…

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Q: II. MULTIPLE CHOICE: Choose the correct alternative that satisfies the given question. Write your…

A: We have to find correct option for the given questions.

Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x - y)dy for the given path. C: x =…

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Q: Describe the graph of the equation. r = 2 sin 10t i + 2 cos 10t j O It is a circle of radius 10 in…

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Q: POSSIBLE P 20 22 24 26 28 h(x) 10 14 11 17 15 9. The table above gives select values of the function…

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Q: Evaluate the triple iterated integral. r2 xyz dx dy dz

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

A: Find your answer below

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

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Q: 2x 1- cos x Graph f(x) = sin for Osxs2x by using transformations. 2 2- Use the graphing tool to…

A: To find: the graph of sin2x2 = 1-cosx2 for 0≤x≤2π Graph of cosx will be as following

Q: Find V (F x G), if F(x, y, z) = 11xi+j+13yk and G(x, y, z) = xi + yj – zk. %3D V. (F x G) =

A: Given,            Fx,y,z=11xi+j+13yk and Gx,y,z=xi+yj-zkTo find : ∇·F×G

Q: 4) Find the critical points of the parametric equations x = t* - 1 y = t3 - t

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Q: What is the point at which the lines x = 3 - t, y = 2 + t, z = 5t intersects with x - y + 2z = 9 ? О…

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Q: 8.) A box with a square base and no top must have a surface area of 48 square inches. Find the…

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Q: Refer to the graph below. Find lim f(x). 3. 2- 1+ -5 4-3 -2 -1 -1+ 3. 4 5 x -2+ -3+ Does not exist 4…

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Q: Sketch the region R and evaluate the iterated integral F(x, y) dA. (1 - 2x + 8y) dy dx 2.0- 2.0 1.5…

A: A detailed solution is given below

Q: 5 4 3 1 -1 T/2 3T/2 -2 -3 - -4 -5 The graph of the function f(x) = csc x is given above for the…

A: The graph of the function fx=csc x is given for the interval x∈0, 2π. We have to find one-sided…

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

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Q: In(2+x) lim, x+-1 X+1

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Q: What is the angle between the vectors u = and v = ? 213° O 188° O 111° 120°

A: Solution:

Q: Find curl (8z i + 9x j + 8y k). curl (8z i + 9x j + 8y k) = ( i )i + ( i )j + ( i )k

A: We know: Where P, Q and R correspond to the components of a given vector field:F→=Pi→+Qj→+Rk→ curl…

Q: Describe the domain and range of the function. KX, y) = 9x2 - y

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

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Q: ||r'(t) x r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = 8 cos(8t)i+8 sin(8t)j+ 5tk…

A: The given formula is: κt=r't×r''tr't3 And rt=8cos8ti+8sin8tj+5tk

Q: 2 - (2x 3y)dx - (2y + 3x)dy 0

A: 2)-(2x-3y) dx-(2y+3x) dy=0dydx=(2x-3y)-(2y+3x)dydx=3y-2x2y+3xdydx=3yx-22yx+3y=vxdydx=v+xdvdx