Sometimes it is possible to solvea nonlinear equation by making a change of the dependent variablethat converts it irto a linear equation. The mast important such equation has the form +pl0y = q(f)y" and is called Bernoulli's equation after Jakob Bernoulli. If n+ 0. 1, then the substitution v = y reduces Bernoulli's equation to a linear equation. Solve the given Bernoulli equation by using this substitution. ty + 7ty- y = 0,r > 0

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 8. dx : (1 – ...

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Q: ate the limit, if it exists. (If an answer does not x2 + 4x lim x-7 x2 - - 3x - 28

A: We will find the limit. 

Q: f(a + h) – f(a) a. Use the definition młan = lim to find the slope of the line tangent to the graph ...

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (– 1)k+1 Σ 5k ...

A: The series ∑k=1∞1kp is divergent if p≤1 and convergent if p≥1 by P-test. A series ∑k=1∞ukis said to ...

Q: IV. Translate into equation. 1. xexceeds y by 2. 2. The sum of x and y amounts to 10. 3. Five more t...

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide ...

Q: What is the particular solution of 2xyy' = 1+y2 , when x =2, y = 3

A: The given differential equation is solved below in detail.

Q: 2.(D³ – 2D³ 2D² – 3D – 2) y = 0

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Q: Identify (a) the point(s) of inflection and (b) the intervals where the function is concave up or co...

A: From the graph: the inflection point: (0,-1)  

Q: e dx PROBLEM 2: J 5e -4 2 csc" wdw cSC PROBLEM 3 : 1+cot w

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Q: Evaluate. Show all your work 1 dx 1-x²

A: By see this solution in below

Q: AD = and BD = . Find a vector perpendicular to both A D and 2A D - BO O O O O none of the above

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (– 1)k+1 Σ 5k ...

A: Please refer to the image below

Q: inlメ- Vx?+* ) X→ め

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Q: Given the ellipse x^2/16+ y^2/4=1. What is the area of the largest rectangle that can be cut from th...

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Q: -dx In 5

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Q: as neatly as possible. Show computations y equation.

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Q: Find the solution of the given initial value problem in explicit form. 1 y/ = (1 – 5x)y² , y(0) %3D ...

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Q: 18. What is the integrating factor of the differential equation y' =cscx-ycotx ? a. tan x C. sinx b....

A: This is a question related to differential equation. Based on the formula of integrating factor we w...

Q: -de 2. S e-x+e*

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Q: Find the local maximum and minimum values and saddle point(s) of the function f(x, у) %3 ху — 2х — 2...

A: Suppose that x, y=a, b is a critical point of fx, y,and Dx, y=∂2f∂ x2∂2f∂ y2-∂2f∂ x∂ y2. Then, If Da...

Q: If 1=- and V= 250 volts, R = 50 ohms. Determine the change in I resulting from an R increase in 1 vo...

A: Given I=VR   , V=250 volts     , R=50 ohmswe want to determine the change in I when   ∆V=1 volt  ,  ...

Q: Find the average rate of change of the function f(t) = 24t from t 5 to t 7.

A: Given     f(t) = 24 t²  

Q: 5. Find the differential equation of the family of straight lines with slope 1. с. у-1-0 d. y' +1=0 ...

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Q: Obtain the differential equation of the family of circle with center on the x-axis

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Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

A: Convergence of series

Q: Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for ...

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Q: Find

A: We will solve find the anti derivative or integration. 

Q: 4. One -third of x is square of the cube root of y. 5. The square of half of x is 1 greater than twi...

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Q: 18. Identify the surface that corresponds to the equation 100y^2 - 25x^2- 4z^2 = 1. show solution

A: It represents hyperboloid. 

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A: Please refer to the image below

Q: 5. y" + y = sec x tan x

A: This is a question of differential equation.  Total solution of the DE is combined of complimentary ...

Q: Solve the given initial value problem. 6x³y + y? 2x6 + 3xy' dy y(2) = - 3 dx O xy - y = 261 x®y² – x...

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Q: EVALUATE: 2 А. (1+j)4 +j3 B. j 1-j²

A: Topic:- complete number 

Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say ...

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Q: Determine whether the series converges using the Ratio test. The series converges eTextbo diverges

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Q: 15. The integrating factor to (2y? +3xy – 2y + 6x)dx + x (x +2y – 1)dy = 0, to make it an exact diff...

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. If the differential equation ...

Q: 12 | In xdx 5 a) Find the smallest K such that | f4) (x)| < K for 5 <x< 12. b) Use the part (a) answ...

A: Let's find. 

Q: By using the method of undetermined coefficients, find the complementary function (y.) and particula...

A: Roots are imaginary then complementary function is e-2x (Acos(√5) +Bsin(√5))  And y(x) =complementar...

Q: Question 13 Evaluate: (6x2– 6x + 6) dx A 10 96 12 - 16 E None of the given choices

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Q: The initial weight of a starving animal is Wo. Its weight after t days is given by W=Wo e -0.005t Wh...

A: We will find the remaining % of wieght as follows.

Q: Find the limit. (If the limit is infinite, enter 'oo' or '-co', as appropriate. If the limit does no...

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Q: Write the first five terms of the sequence: |{Vn² +7n Determine whether the sequence converges, and ...

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Q: 4k+2 7ペ-1 k=1

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Q: 4x + 2x + 3. If Ax 0.1 at x = 5, use Let y = linear approximation to estimate Ay Ay 2

A: A detailed solution is given below

Q: Find the solution of the given initial value problem. ty' + 3y = t – t + 5, y(1) = 3, t > 0 y = ||

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Q: b. Which, if any, of the above changes in population can be modeled by a linear function? Show all w...

A: Given:   

Q: Approximate the area under the graph of f(x) over the specified interval by dividing the interval in...

A: f(x)=0.015x3+4 ;  interval -6,0 ; 3 subintervals

Q: The equation of a circle is given below. Identify the radius and the center. Then graph the circle. ...

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Q: The following situation applies to the attached question The fluid pressure (in atmospheres) at the ...

A: Px,y = 1+ x2y10Where, P : Fluid pressure in atmosphere at the bottom of a body of liquid of       va...

Q: A point starts at the location (6, 0) and travels 15 units CCW along a circle with a radius of 6 uni...

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