what is the derivative of y=e^-1/2x(C1cos3x+C2sin3x) and evaluate if x=0, y'=8

Q: 8. (e* + y)dx + ( 2+ x + ye' )dy =0

A: Given:- (ex +y) dx +(2+x+yey ) dy=0 To find:- General solution for given differential equation

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Q: 4а — 2b — Зс + d — 3 2а - 2b — 5с %3D — 10 || 4а + b + 2c +d — 17 За + с + d — 12

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Q: d The power rule for finding derivatives is dx for all exponents n. 9 as 9Vn for some n. V In order ...

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Q: 1. Each situation relates a quantity and a price. Calculate the two different unit rates associated ...

A: Use unitary method.

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Q: On which interval does the function f(x) = (x+ 5)/(x-1) discontinuous? О а. [0, 2] O b. [-1,0] Ос. (...

A: Note: As per our company guidelines we are supposed to answer first three questions only. Kindly ask...

Q: Solve the differential equation 2xyy' = 1 + y". If y = 3 when x = 2, determine y when x = 1.

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Q: ii. 0.9,0.99,0.999, 0.9999,..

A: This can be written as  9/10, 99/100, 999/1000, 9999/10000..... (10-1)/10, (100-1)/100, (1000-1)/100...

Q: л3 160х - 3x? - 2ху- 2у? + 120у -18

A:

Q: 1. Find the limit of the following: x° – 11x +37x* +6x' – 297x? +621x – 405 lim. x* —11x* +47х* -114...

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Q: Eliminate the arbitrary constants b^2 x^2 - a^2 y^2 = a^2 ^b2

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Q: 3. Find the 8th term in the binomial expansion of (x² + y³)10. correct combination, evaluating combi...

A: We will find the 8th term. 

Q: III. Use the nth-Term Test for divergence to show that 00 n +10 n=1 is divergent, or state that the ...

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Q: Determine the particular solution of y"– 3y'+2y= 4e"; y(0)=-3,y'(0)= 5 using Laplace and Inverse Lap...

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Q: No, last te 10

A: FOLLOW THW PROCEDURE GIVEN BELOW.

Q: Find the general solution of = 0 y" – 2y"' + 10y":

A: Given: y(iv)-2y'''+10y''=0To find the general solution of given differential equation:General soluti...

Q: x2n+1 Given the Maclaurin series for sin x is sin x = E=0(-1)". find the Maclaurin %3D (2n+1)!' seri...

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Q: Determine whether the integral is convergent or divergent. 1 dy 1 4y convergent divergent If it is c...

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Q: Exact Differential Equations (16) (17) (2xy + 1)dx + (x² + 4y)dy = 0 (18) (6xy + 2y² – 5)dx + (3x² +...

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Q: A plane flying horizontally at an altitude of 1 mi and a speed of 540 mi/h passes directly over a ra...

A: Solved below

Q: If ã = <!,2,37 and b=<5,0 -17, find the vector pojection of %3D %3D ŏ onto à.

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Q: 2. Nhat is the value of n for the row of Pascal's Triangle that is: 4 1 6 4 1? correct value of n) W...

A: Follow the procedure given below. 

Q: Evaluate the given function · sin2ØdØ 1+sin?ø a. In[In(1 + sin²Ø)] + C b. In[1+ sin²Ø]+C c. In[sin2Ø...

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Q: A. Evaluate each of the following indefinite integrals: S*(1+v*) -ldv (cor-ly2) 2.

A: Solution is given below:

Q: Suppose 1000 people enter a chess tournament. Use a rooted tree model of the tournament to determine...

A: Let a1, a2, a3, a4, a5,....................................a1000 are the participant. As per rooted ...

Q: 12. Use the factor Hheveto determine whether x-C Isa fultol. offd.

A: (11). The given function is: f(x)=x4+8x3+12x2 ;       x+1

Q: Q: A Fraction becomes 4/5. If 1 is added to both numerator and denominator.If, However 5 subracted f...

A: Solution Given that If we add 1 in both numerator and denominator then we get a fraction 4/5. And i...

Q: n! %3D an 2n

A: We have to check weather the given sequence is increasing, decreasing and neither in nature.

Q: Find the equation of the tangent line T(x) to the graph of the given function at the indicated point...

A: Given, y= 2x/(x-1) By differentiating we get the slope of tangent.  

Q: %3D cosx cotx sin x CSCX

A:

Q: 3. feVin e+2ln² e +ln€ de

A: The given integral is: I=∫θ-1ln3θ+2ln2θ+lnθ dθ

Q: y = Arc sin e

A: Follow the procedure given below.

Q: y" + yW – 9y" – 13y" + 8y' + 12y = 0

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Q: The average change of a function f over an interval [æ1, x2] is f(m2)-f(#1) First find the average r...

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Q: Homogeneous ODE x^2y'=4x^2+7xy+2y^2

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Q: Find an equation of the plane containing the points (0,0, 2), (2, 4, 1) and (–2, 3, 3).

A: Equation of a plane containing 3 points is x-x1y-y1z-z1x2-x1y2-y1z2-z1x3-x1y3-y1z3-z1=0  

Q: At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing no...

A: In this question we have to find how fast is the distance between the ships is changing at 4:00 PM.

Q: The height (feet) of an object moving vertically is given by s = - 16t2 + 144t + 108, where t is in ...

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Q: 10. y(2x3 -x?y + y³)dx - x(2x³ + y³ )dy = 0

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Q: The distance from the point (-1, -2, 3) to the line x = 1 + 2t, y = 2 - t, z = 3 - 2tis [a] (input e...

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Q: 4x-12y+7z=10 x-4y+2z=4 -4x+11y-7z=-6 Use the gauss method and show every step please

A: The given system of equations,4x-12y+7z=10x-4y+2z=4-4x+11y-7z=-6

Q: 4. A metal is heated up to a temperature of 5000C. it is then expose to a temperature of 380C. after...

A: (4) Given that , Initial temperature = 500°C T0=38°C After 2 minute temperature = 190°C Evaluate whe...

Q: Determine whether the following sequence is increasing, decreasing, or neither. 5n-2 i. an = 4n+1 ii...

A: ?As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly repost oth...

Q: 1. Evaluate (b) (-2+ j6) - (3- j2) and show the results on an Argand diagram. (a) (3+ j2)+(5- j) and

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Q: Write down the first five terms of the following recursively defined sequence. a1 = -5; an+1= -2a, +...

A: Given sequence is  an+1=-2an+5with a1=-5To find the first five terms:  

Q: Variable Separable (6) (xy -3y +x – 3)y' = xy + 2y - x- 2

A: As per our guidelines we are supposed to answer only one question.kindly repost others question as a...

Q: Vrite out the first five terms of the sequence with, In(n) n+1 determine whether the n=1 sequence co...

A: We will find the limit