y = cje* + cze²r y" -y – 2y = 0 O 2y " -y' – y = 0

Q: Q2) Show that y = 35 x* – 30 x² + 3 satisfies ( 1– x² )y" – 2xy' + 20y = 0 %3D

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Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = x0 and then find the nth Taylo...

A: This question is based on Taylor series.

Q: What is the value of 7/2 x(3 cos(x) + sin(x))dx ? 7/2 Give your answer as an integer or as a decimal...

A: Given I=∫-π2π2x(3cos(x)+sin(x)) dx To evaluate the Integral I :

Q: 9. Evaluate f(e* + 2*) dx a.) 2e* + +C In2 b.) er + 2ln* + C c.) e* ++c d) e* + 2ln x + C In2 10. Ev...

A: Evaluate integrate. And follow step 2nd .  According to guidelines we solve only first three parts. 

Q: Find the derivative of the function. f(t) = 8r2/3 - 4t/3 + 8 f '(t)=

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) xp J xV81 - (In x)²

A: topic ,- indefinite integral

Q: (9cosx+y°cosx) dx +2ysinx dy = 0, y(5)= -4 the value of the constant (c) of this D.E will be:

A: Solution is written in below steps.

Q: хdу + (у — ху + 2\dx — 0 %3D

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Q: (2x² +)x ;dx (x8 + 4x5 + 4x²)² Using u-substitution and transformation of the integrand, then the po...

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Q: Consider the following system on (-1,∞0) × (–1, 0), 2y 2x 1+ Y 1+x 1. Find all the equilibrium point...

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Q: 7. Read about the Integral Test in Section 11.3 and, specifically, through example 2 to see how the ...

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Q: Find the radius of convergence of the power series. (If you need to use co or -00, enter INFINITY or...

A:

Q: dx 6. Evaluate 5-16r

A: Evaluate ∫dxx83-16x2

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

A:

Q: 58. Find the maximum volume of a cylinder inscribed in a core of 4 m volume.

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Q: Find f(x) so that when u = f(x) the integral J 1+ In x tan(f(x)) dx can be rewritten as cot u du..… ...

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Q: The function f(x, y) : 1+2? +y? is 1-x2 -y? discontinuous at the points {(x, y)\æ² + y² # 1}. True F...

A: f(x,y)=(1+x^2+y^2)/(1-x^2-y^2)

Q: A cylindrical container with circular base is to hold 64 in^3. Find its dimensions so that the amoun...

A:

Q: 48. h'(x) if h(x) 2+9

A: Here, the given function is: h(x)=e2xx2+9 To find the first derivative of h(x), using the quotient r...

Q: p-

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Q: Solve using the U-Technique Question 19 1+ In x Find f(x) so that when u = f(x) the integral tan( f(...

A: Here, given that when u=f(x), ∫1+ln xtan(f(x))dx=∫cot u du⇒∫1+ln xtan(f(x))dx=∫1tan u du

Q: 2. Given: a, = 5, a4 = 14 Find: az =? а. 7 b. 8 с. 10 d. 12

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Q: Find the amplitude, period, and horizontal shift of the function. y = -3 sin(6(x +)) amplitude perio...

A: Given query is to find the period amplitude and the horizontal shift.

Q: The population model given in (1) in Section 1.3 dP = kP dt dP or (1) dt fails to take death into co...

A:

Q: 12. Evaluate ((1– cos x) dx a.) 1- sin x +C b.)x - cos x +C c.) 1- cos x+C d.) x- sin x+C 13. Evalua...

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Q: 2:(y-x² )dx+ dy =0 1.

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Q: on 3 of 9 cies empt History Correct. y method to determine whet

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Q: Find the derivative of the function. (t) = (9t + 14)2/3 6 f '(t) = (9t + ly)1 3

A: Given that        f(t) = (9t + 14)2/3 Here we have to find f'(t) .

Q: Which of the following is true about horizontal asymptotes? OAll rational functions have at least on...

A: Find your answer below 

Q: liminate the parameter to find a Cartesian equation of the curve. =(t) = - 3 + 2 cos t (t) = 2 sin t...

A: Topic:- function

Q: y = Vx – 7 ,(7,0) -

A: Solution is written in below steps.

Q: y6_y²+7 h (y) y2+3y

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Q: (2x + dx + 4x*) (x +4x5 Using u-substitution and transformation of the integrand, then the power for...

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Q: 2. Find the imit lifany) メー5 X-25 lim X25

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Q: Solve the given differential equation by undetermined coefficients. y"- 2y' + 2y e2*(cos(x) – 8 sin(...

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Q: Find the indefinite integral. (Use C for the constant of integration.) |zV 16z2 - 81 zp

A: ∫1x2+a2 dx = 1aarc tan(xa)+C

Q: Consider the expression ſ V4 – x² dx = F(x)+C. The expression %3D F(2) – F(-2) is equal to

A: Here we have to evaluate F(2)-F(-2)=? We have, ∫4-x2dx=F(x)+C

Q: Determine whether the series converges. k 'In(k + 9) The series converges. O The series diverges.

A: Given query is to find series converges or diverges.

Q: 1. 2x(y-x dx+ dy = 0

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Q: Find the indefinite integral. sinh(2 – 7x) dx Step 1 First, let u = 2 - x. Now, differentiate u with...

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Q: Find the radius of convergence and the interval of convergence. k (x + 3)* k=0

A: The summation of (5/7)k (x+3)k ; k from 0 to infinity.

Q: Determine whether the series converges, and if so find its sum. 4k+2 Σ 7k-1 k=1 1) This series can b...

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. 8 k! k = 1 Identify a...

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Q: Find the Taylor polynomials of orders n = 0,1, 2, 3, and 4 about a = x0 |and then find the nth Taylo...

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Q: EXERCISES 1. What value(s) of c, if any, will satisfy the IVT for the given function f and the given...

A: topic - intermediate value theorem

Q: Problem 2: A piece of string whose length is given below is cut into two pieces. One piece is used t...

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Q: Find the solution of the following Differential Equations 1) ydx+ xdy 0 2) (xdy- ydx)/x = 0

A: Find your answer below 

Q: 1. S sin’y (2 – 3 cos y)°dy

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Q: Find the differential equation whose solution is given by y? = 4ax ydx – 2xdy = 0 O ydy – 2xdx = 0

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Q: Given h(s, t) = s In t – t ln s. What is the value of h(e, 1)? %3D

A: topic - functions