Solve the given initial value problem. 6x³y + y? 2x6 + 3xy' dy y(2) = - 3 dx O xy - y = 261 x®y² – xy³ = 630 549 O xºy? + xy³ = 522 O xy? + xy = 234

Q: g(x) = = ax + C, where a ER Power: is continuous on [a, b], differentiable on (a, b) and g'(x) = f(x...

A: Given: the graph of function F which is an antiderivative of the function f FIND: (a) list critical ...

Q: Prove that ∀n ∈Z, gcd(7n + 1, 15n + 2) = 1 *use only the definition of divisibility and gcd please!

A: we want to prove that   gcd(7n+1 , 15n+2)=1

Q: he price, in dollars per units, that consumers are willing to pay for a popular high-end digital cam...

A: Price

Q: (3x +1, xs0 f (x) = {x,0 < x <4 x – 5,x 24 2 6. Given , evaluate f(3). O f(3) = 9 O f(3) = 10 • f(3)...

A: Given query is to find the value of the function and at x = 3.

Q: Let f(x) = (x + 7)² Find a domain on which f is one-to-one and non-decreasing. Find the inverse of f...

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Q: dive ges. If it conve ges, find the Determine whether the seavence converges or n+1o Sin(n) 3n+ 2

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Q: convert rectangular coordinates(-2,0) into polar form.

A: Given Cartesian co-ordinate point (-2,0) 

Q: Differentiate. sin(0) f(0) 1 + cos(0) f'(0) %3D II

A: Differentiate 

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Q: Evaluate the indefinite integral. 24 W cot(x) csc2(x) dx 24 cot?(x) + C 25 O (csc(x))24/25 + C 24 25...

A: To solve this use integration by substitution method

Q: At 10:17 a.m., you pass a police car at 55mph that is stopped on the freeway. You pass a second poli...

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Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as an imprope...

A: The series resembles 1/n^2. So, it is convergent.

Q: Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable ...

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Q: Evaluate the integral f 2x (x² + 5) dx using the substitution 13 u = x +5. 2x (x² + 5)*° d =| +C

A: I =∫ 2 x (x2+5)13 dx  u = x2+5du = 2x dxI =∫ u13  du We know that,∫ xn  dx =xn+1n+1+C

Q: For the function f (x) = 1 - 1                                       (x +2)2 ,  find the following ...

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Q: 6. Consider the function f(x) = In(x + 2) – 2 arctan(x) a. Find all critical points in the domain of...

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Q: -x2 + 5x + 14 Evaluate lim x-2 -5x2- 2x + 16 Submit an exact answer.

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Q: 7. Including complex zeros find all zeros of f(x) = 9x° + 57x² + 66x + 30

A: We have to find the zeros of the given polynomial.

Q: If z(x, y) = 3x + 4y , x = t² and y = 2t. Determine the value of t where dz = 0 dt answer: 5.

A: Solution:  

Q: Let f (x) and g (x) be antiderivative of h (x), The which of the following is true? A None of the gi...

A: Application of derivative

Q: 1 Describe how the graph of the function g(x) = |x| -7 can be obtained from the basic graph. Then gr...

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Q: Solve the given differential equati1on. All solutions should be found. dy 25 – 2y dx NOTE: Use c for...

A: The given differential equation is; dy/dx=(x5-2y)/x2.

Q: Consider the following sequence: {an} = {n – n² },e n=1 Use an+1 – an to show that the given sequenc...

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Q: dx V9-x2

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Q: Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied. xy...

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Q: Find the slope-intercept form of the equation of the tangent line to the curve defined by fla) = 3-2...

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Q: Express the repeating decimal as a fraction. 0.1111. . .

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Q: 6. Find the unit vector for which the directional derivative Duf(x,y) of f(x,y) = %3D 3x2 + 4y2 at t...

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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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Q: Co you %3D 1. Find fr and fy for fla,y)= cos (24) fx= cos (xy). Lx"- (-sin (xq)- y) - (-sin (xy)- y?...

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Q: 10 8 4 6. 2. 2.

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Q: Find an equation of the line passing through the pair of points. (4, 3), (-4, –4) Sketch the line.

A: We can find the required equation of line passing through the pair of point is as below.

Q: 15. Use the following table to answer the question below: 3. 4 6. 7 4 6. (a) Is Da function of C? Re...

A: Given table:- C 3 4 5 6 7 D 2 4 6 4 2     To find:- (a) Is D a function of C?  (b) For this ...

Q: Evaluate the integral. Do NOT use inverse hyperbolic functions as your final answer. 1 x* + 6х + 7

A: ∫1x2-a2 dx = lnx2-a2+x +C ; where 'C' is an integration constant.

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

A:

Q: Determine the form of a particular solution for each differential equation. No need to solve for the...

A: Given that the differential equation is      2y"'-3y"-3y'+2y = (ex+e-x)2 

Q: Find an equation of the line passing through the pair of points. (4, 3), (-4, –4) Sketch the line.

A: We can find the required line as below.

Q: 1. Find the following limit, if it exists. lim (z.1)-(0.0) V2 + y? +1-1

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Q: Consider the function (T) 12z mean slope of the function on this intervat. 30r 10 on the interval 6,...

A: Average or mean slope is fiven by f(b)-f(a)b-aThe value of c can be calculated byf'(c)=f(b)-f(a)b-a ...

Q: c. Consider the function h(x) = 0.4 sin(0.8x) + 6. i. What is the period of h? radians Preview ii. W...

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Q: If the polynomial f(x)=2x³ +3x²+3x+2 is expressed as f(x)=a,Po(x)+a,P1 (x)+a2P2(x)+23P3(x), then a1 ...

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: -. Solve the differential equation: (D – 3) (D² + 3D + 2) = 0, where D is the differential operator ...

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Q: 10

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Q: Let T: R² → R³ be defined by T((a, b)) = (a, a + b, a + 2b). Find range T and a basis for range T.

A: Given:    T(a,b) = ( a , a+b , a+2b )

Q: Find the solution of the given initial value problem. 3 y = t Cos t t-3 y(T) = 0, t>0 y(t) =

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Q: f(z+h)-f(x) For f(r) V7z 1 37, findf (z) using the definition f '(z) = lim h30 h "(z) sing this, fin...

A: Given query is to find derivative by definition and equation of tangent.

Q: Vw² – 2w +3 lim W +5 W→-00

A: limw→-∞w2-2w+3w+5

Q: 1+5x lim 2-3x X→+∞

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Q: - Beta Function ; Evaluate the following integrals : d z (2+bz?)² C. SuD 5/4 3/4 2.

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Q: The pressure, volume and temperature of an ideal gas are related by the equation 8.31T P(T,V) = V Wh...

A: Given, P(T,V)=(8.31T)/V At centre V=12litre and T=310k