Which of the following is correct? * 3 3 (3 In(x²)) = dx (3 In(x²)) = dx Option 1 O Option 2 d 6 (3 In(x³)) = (3 In(x³)) = dx dx Option 3 O Option 4

Q: 3. (a) y(8) when y=cos 2x 2 (b) y(9) when y=3 cos t 3

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Q: 1. 12a – 92² + 2 dæ

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Q: Exercise 195 Further problems on Leibniz's theorem 7. Given 2x2y" + xy' +3y = 0 show that 2x2y(+2) +…

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Q: Find the distance traveled after 6 seconds by a particle whose velocity is v(t) = (t − 2) meters at…

A: Given

Q: Find the following quantity if v 2i – 3j + 4k and w = - 2i+ 4j- 4k. 4v + 3w ... 4v + 3w = (…

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Q: 6. What can you conclude when dy is changing dx from positive to negative? A) fis at a local minimum…

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Q: 6. Evaluate the following: (ey)dy dx 0. A. e-1 e-1 C. 2e +7 2. D. e?

A: Given: I=∫01∫0y3exydydx   As we know the basic integral formula; ∫eax+bdx=1aeax+b+C

Q: (D* – 1) y = 0 O y = cje* + cze* + c3 cos x + c4 sin x O y = cje* + czxe* + C3x? cosx + C4x³ sin x

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Q: Find the derivative of the following function F(x) (2t – 1)' dt

A: To find the derivative of the following function.Fx=∫x2x72t-13 dt

Q: f(x) = 2x2 +1

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Q: y= v16-x -4 -2 2

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Q: polar com 2) (3, 240°) 90° 120° 60° 150° 30° 0- 180° 2 3. 330° 210° 300° 240° 270°

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Q: Use the theorem of Leibniz in the following problems: 1. Obtain the n'th derivative of: x2y [x²ym) +…

A: To find out the nth derivative of the function.

Q: : Find f(t) ( Inverse Laplace Transform )of the following functions s+1 1. F(s) 2.F(s) (s +2)+n?n2…

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Q: 13. Evaluate: sin(x²) dx A) 2x cos(x2) B) 2x sin(x?) C) 2x cos 2x D)2x cos x 14. Find the derivative…

A: To find Evaluate the integral:

Q: The volume generated when the region bounded by y = x , y = 1, x = 0 is rotated about x - axis is…

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Q: Consider the following initial-value problem. 4 f'(x) f(9) = 31 %3D Integrate the function f'(x).…

A: We have to find the function.

Q: (メ+ッ)dx + (x4ッ)dy =0 dx dy x yz x?y

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Q: The area between the curves f(x)=x and g(x)= x^2 on interval [0,2] O 2

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Q: solve

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Q: finfyiy-6)"dy 2. 2.

A: We have to solve given integral.

Q: 4. Which of the following is the maximum value or the minimum value of the graph of polynomial…

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Q: = 1 and z = g(x, y) > 0. Determine gz 23 2/2, Suppose 3x2 + 2y² + z2 and gy 2/3' 2/2

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Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 16 + x²-y²…

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Q: In ly-y-cf dy

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Q: Let y = tan find the differential dy of the function.

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Q: Identify the type of quadric surface defined by the equation 6x² + 3y² + 2z² = 36, and find all x-,…

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Q: A. Set up the double integral I |(2² + y² )dA where R is the region above the a-axis bounded by the…

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Q: Exercise 195 Further problems on Leibniz's theorem 5. Find an expression for y(4) if y =e'sin t.

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Q: 1. Find dy for each of the following: dx 2-x2 a) y= In² 1+x y = Vx+e* c) y = 52r+3

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Q: dy (x-2)° · (2x + if y dx\x=0 Find = e2x . Vx+8

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Q: The velocity, in feet per second, of a running rodent is modeled by v(t) = 5√t − 2t. What is the…

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Q: The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the…

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Q: T/2. 1. Let R be the region bounded by the graph of f(x) - sin x, the x-axis, and the vertical line…

A: Given the region is bounded by the f(x)=sinx2 and line x=π2 and x axis.

Q: Find the center of mass of the region bounded by y=2sin(2x),y=0y=2sin⁡(2x),y=0 on the interval…

A: Given

Q: (x +y) dx +(x+y)dy z o

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve the following differential equation using Laplace transform 1. dx2 d²y + 25y = 10 (cos(5t) – 2…

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Q: 5.) What can you conclude when dx is changing from negative to positive? A) fis at a local minimum…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: (ax-2) dx x2+ 2X + 15

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Q: Part A. Evaluate the following limits using L'Hospitals Rule, algebraic manipulation, logarithms, or…

A: Note: According to our expert guidelines only first three subparts are to be answered kindly repost…

Q: 7. (a) y(4) when y 2ln 30 1 (b) y() when y= %3D In 2t %3D

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Q: Evaluate the integral Se*dx

A: We can solve this as follows:

Q: Sketch the graph of f(x) = 2x + Vx*.

A: Given that we need to Sketch the grah of  y = 2x1/3 + x4/3  Now,  The graph is as follows

Q: d (7 ln(x)) dx Find

A: Find

Q: 5. Use the shell method to find the volume of an ellipsoid formed when that part of the ellipse x2 +…

A: Given

Q: Differentiate each function. Simplify as much as possible and express all answers using positive…

A: As per bartleby guidelines we only give first three question answers.  Let's find all…

Q: Consider the function f (x) = sec (e*). %3D o How many different functions are composed to get f…

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Q: 22-23. The top of a 25-foot ladder is sliding down a vertical wall at a constant rate of 4 feet per…

A: According to our guidelines we can answer only one question or three subparts of a question. Other…

Q: : Use PARTIAL FRACTION DECOMPOSITION to find -1 dm т2-6т-7

A: We have to find integrating using partial fraction.

Q: Find the dy/dx: Given tan (x²) y =

A: Differentiate with respect to x.