Use the formulas of Derivative of the Algebraic functions and Logarithmic functions in determining the derivative of the following function.. а. у b. Find y", given y = e In x. c. y = In (x + V1 + x'):

Q: y + Jx? +yz dx = xdy when x-13', y=I when x=J3, y=| 4.

A: Homogeneous differential equation : A differential equation of the form f(x,y) dy = g(x,y) dx is sai...

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A: Given: y=5x2

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A: Explanation of the answer is as follows

Q: using undetermined coefficients (D^2-2D+2)y=24e^x sin3x

A: Given: (D2  -2D+2)y=24ex sin3x

Q: 18. If x? – xy + y? = 3 find y" (second derivative) %3D 18 12 12 18 В. (x – 2y) C. (x – 2y)² A. D. (...

A: Given:- x2 -xy +y2=3 To find:- y'' 

Q: Elminote the orbitrary constants X =k +ct, y= ct² Find the differenhal equation of the

A: Given: x=k+ct; y=c2t2To form a differential equation by eliminating arbitrary constants  

Q: Multiples of 7 are written next to each other 714212835.... Find 2020th digit. A) 1 В 3 C 5 D 8

A: Given:- Multiples of 7 are written next to each other 714212835.... Find 2020th digit.

Q: y(2x3 -x2y + y3)dx – x(2x³ + y3 )dy = 0

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Q: 1. State the Chain Rule: a. z= f (x, y) is a differentiable function and x = s(t), y = p(t) - are fu...

A: Given z=f(x,y) To state the chain rule

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Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the b...

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Q: A function f(æ) and interval [a, b] are given. Check if the Mean Value Theorem can be applied to f o...

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Q: What is the largest interval in the function f(x) = x² - 2x + 1? A. (-∞, 1) B. (-∞, 0) C. (1, ∞) ...

A: Function -  parabolic function    Option A is the correct option.

Q: Find all solutions of the linear ODE: y'''+y=t

A: I am attaching image so that you understand each and every step.

Q: 3+ -5 -4/-3 -2 -1 1 2 34 5 -1 -2 -3+

A: The shape of the curve that represents a polynomial with even degree has is one sided. I.e the both ...

Q: Evaluate the improper integral Xe* dx Ina A) integral diverges ৬) C) o D) Inz In2 2

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Q: Given Cost and Revenue functions C(q) = q° - 8q + 51q+ 5000 and R(q) = - 3q +2400q, what is the marg...

A: Given query is to find the marginal profit on production level of 60 items.

Q: orth0gonal trajectories y^2=4x^2(1-kx)

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Q: O Find dy/dx, given y =. -u and u =TR42.

A: NOTE: Refresh your page if you can't see any equations. . take the derivative with respect to u

Q: Solve cot x-v3 =0 over [0,2t)

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Q: The curve y+1=x< is rotated about x-axis. Which of the following is/are true? O A. V= 16TT /15 O B. ...

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Q: dQ where Q = V3x“ + dt + 3y² Use the Chain Rule to find +z", x= sin t, y= cos t, and z= sin t. dQ %3...

A: Given query is to find derivative using chain rule.

Q: Please all solve the issue but don't copy

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Q: 8) If the graph of function f(x)=(1- ax)3/X?crosses its oblique asymptote at x=1/3 determine the val...

A: NOTE: Refresh your page if you can't see any equations. . use the formula 

Q: dx 1+ ×°yス 2Y - 1+(xy)². 2x + X

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Q: Solve log æ = 1 – log(æ – 3). If there is more than one solution, write the numbers in ascending ord...

A: Given that, The equation is following, log(x) = 1 - log(x - 3) we have to find the solution of this ...

Q: dx Assume that x = x(t) and y = y(t). Find using the following information. dt dy x2 + y? = 2.92; - ...

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Q: Lauren plans to deposit $7000 into a bank account at the beginning of next month and $250/month into...

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Q: Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to...

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Q: 9. There is an infinite discontinuity at x = 0 and f(0) = -2 10. There is a jump discontinuity at x ...

A: 9. There is an infinite discontinuity at x=0 and f(0)=-210. There is a jump discontinuity at x=1 and...

Q: This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrang...

A: I am attaching image so that you understand each and every step.

Q: 2y 9. . dx x -4 (x+2)? x² -4

A: This question is based on solution of linear differential equation.

Q: da Evaluate 2 (16 + x2)*

A: ∫1(ax2 + b)ndx = 12b(n - 1)∫2n-3(ax2 + b)n-1dx + x(ax2 + b)n-1

Q: dx =(x²yeº- 3xy²) dy |

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Q: Il only I and III only I and II only

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Q: 3 V9x2 + 4+2 In 4 1 dx 3x

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Q: written

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Q: 3rd-Quarter... 4. Focus (3, 0) 5. Focus (-5, 0) 6. Focus (0, 10) 7|Page 1- Given the falowing condit...

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Q: Consider the following sequence: 9" {an} %3D 4n2 n=1 An+1 to show that the given sequence {an} is st...

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

Q: Carite tan 24t.10x= 14 equlin fer a lie pepanicubr to Hhe pait (10.6) and

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Q: (3y²-x 0 ;when x = 1, y = 1 2y4

A: This is homogeneous Differential equation 

Q: y Iny Ae^+ Bex

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Q: rite the nrst erms of sec ice: {Vn² + 2n – n}-1 +oo Determine whether the sequence converges, and if...

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Q: 1. A model for the position x (t) of an Olympic jump skier says that the acceleration a(t) = x" is p...

A: As per as our guidelines i am supposed to answer only three parts of this question Please repost the...

Q: Solve using method of undetermined coefficients. (D2 - 2D + 2) y = 24exsin3x

A: Let's find. 

Q: Find the derivative of y = VT(x + 38). %3D dy dx

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Q: Find the exact length of the curve. y = (2/3)(1 + x2)3⁄2,      0 ≤ x ≤ 2

A: Given: - The curve is, y=23(1+x2)32,  over the interval, 0≤x≤2 To find: - The exact length of the cu...

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Q: and stra ight and x : 8 Let R be an area enclosed by a curve. : 1 Using the cylindrical shell method...

A: Given problem:- Let R be an area enclosed by a curve. X =4√y and straight line y=1and x = 8 Using th...