2. y = (x² – 3)²

Q: Solve the differential equation (xy – 6x²)dy – (2y² – 9xy)dx when x = 1, y = 1

A:

Q: Solve the following equation on (-o, co) 2 cos2 3x + sin3x = 1 %3D

A: Solve the equation 2cos23x+sin3x=1

Q: A ax? +C B a ax +C a?x +C 2 D.

A:

Q: Examples: Find the limits of the following: 1. lim sinx = sin1 2. lim cosx= cos (-1")= 7 x-1* 3. lim...

A: 1) limx-1- Sin-1x 2)limx--1+ Cos-1x 3)limx-infinitytan-1x.

Q: Use any method to determine whether the series converge. 1. (a) 19k k=1 The series 00 1 (b) 19 + 1 k...

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Q: Find an equation for the tangent plane and the normal line to the surface x? + 2y? – 3z² = 3, at the...

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Q: Solve the differential equations x (x- y²- x)dx =y(x²-y²) dy when x=2, %3D y=0

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Q: 4. (D² +D-1)² y =0 ,when x= y = 0, y' = y" =1, y" = -1

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Q: Calculate the volume of a solid on the first octant and under the plane defined by 2x+6y+6z=24. Roun...

A: Let's find. 

Q: Assume that functions f and g are differentiable with f(- 3) = 4, f'(- 3) = - 4, g(- 3) = - 4, and g...

A:

Q: Use any method to determine whether the series converge. (a) 11k k=1 8.

A: "Since you have asked multiple question, we will solve the first question for you. If you want any s...

Q: In the integral, cos?tsin2tdt , the correct u using general power formula is;

A: Given, ∫cos2tsin2tdt Formula: cos2 t =(cos2t +1)/2  

Q: cosh In(x) y%3= VII. xp: If u is a function of x then what is u? u-f(x) A.In(x) du is equal to? A.2x...

A:

Q: (1 + +)' y =

A: As per the instruction, we will be answering only first question.  y'=1+1x3'    =31+1x21+1x'    =31+...

Q: SOLVE THE FOLLOWING DIFFERENTIAL EQUATION (4x3y – 15x2– y )dx +(x4 +3y2– x)dy=0

A: A differential equations of the form, M(x,y)dx+N(x,y)dy=0 is said to be exact iff ∂M∂y=∂N∂x  

Q: x sin(x² )dx 2.

A:

Q: 9. 1+x

A:

Q: Determine the Laplace Transform of the given integral equation. A. f (t) = S sin(t - 7) cos(7)dr

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

A: Here we have to find out the convergence of The infinite series and then we find out the sum if it c...

Q: 11. Evaluate f- 2 sin 3x dx 4+cos 3x a.) -2 In 14+cos3x| + C b.) 3 In 14+cos3x| + C c.) - In 14+cos3...

A: Solve by integration

Q: Given the function: z = e*+y sin (x + y) dz a. Compute the ду b. Compute the dz show complete soluti...

A:

Q: Solve the differential equations by any appropriate method and indicate the method you have used/cho...

A:

Q: (Inºx– 3lnx) +dx (A Inx B Inºx © Intx D In x- 3lnx E In x- 3 (F) None

A: The integral is  ∫ln6x-3lnx4xdx

Q: Solve the differential equation:COsx dx +[sin(x+y) + sin(x – y)]dy=0

A: Given, cosxdx + [ sin(x + y) sin(x- y) ]dy = 0 we have to solve the differencial equation

Q: I. Analyze and sketch the following curves. Indicate critical points and label your graph. 1. y = 1/...

A:

Q: 14. Find the linearization, L(x,y,z) of the function f(x, y, z) = x³/y2 + z² at the pointP,(2,3,4). ...

A: Given that        f(x,y,z) = x3√(y2+z2) 

Q: b) Find the solutions qf th equation 4.1.2 D Ø(D) 1. (D3 – 6D2 + 5D): 2. (4D2 - 3D- 10):

A:

Q: In the indefinite integral J 3x²e* dx, the integrand is A 3r © 3x2 D x³+C B.

A: The given integral,    ∫3x2ex3dx

Q: Which of the following integral will give the volume of a solid generated when the area bounded by y...

A: We have to find volume generated when area is rotated about x-axis.

Q: dy 2y (х + 2)* dx x -4 х - 4 +

A:

Q: Suppose f(x)=6(2.3)x and g(x)=58(1.7)x. Solve f(x)=g(x) for x.

A: Given that        f(x) = 6(2.3)x and  g(x) = 58(1.7)x And given f(x) = g(x)  Here we have to find th...

Q: The graph of a function f is shown. Does f satisfy the hypotheses of the Mean Value Theorem on the i...

A: topic - mean value theorem

Q: etermine each function's domain and range. If applicable, use a graphing utility to confirm the hand...

A:

Q: 1. If x-y? = 25, then y" = %3D a.) b.) c.) - d.) - 2. If y = cos(3x+1), find y' a.) 3 sin(3x+1) b.) ...

A: Given:   (1) x2 - y2 = 25    (2) y = cos(3x+1)

Q: Solve the equation (x + 3y)dx - xdy 0 %3D O y? = 5x4 + cx3 O y = x5 +cx3 O 2y = x5 + cx3 %3D O 2y = ...

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Q: dw 4 Which of the following characterizes the differential equation +v= 0? A 2nd order, 4th degree O...

A:

Q: Solve the differential equation (7х — 4у + 15)dy + (2x — 5y + 12)dx — 0 when x 3D 3, у %3D 2

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Q: Express the repeating decimal as a fraction. 0.2513 23 23 23...

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Q: y- 2x = 3y - 2 %3D Oz= 3yIny +1+Cy Oz= 3lny +1+ Cy Oz = 3y Iny +1+C Oz= 3y Iny + Cy

A:

Q: The distance in feet of a particle from some fixed point is given by the following function, where t...

A: Given function,s(t)=t2+3t-3a)  What is the average velocity of partical from the interval 1 to 2 sec...

Q: : / ain(tun3x)dx cos²3x tan( tan3x) dx Evaluate: A -in|sec(tan3x)| + c 3 B 3 -In|cos( tan3x)|+C O In...

A: On solving this we will get

Q: A certain radioactive material follows the law of exponential growth. If between noon and 2 pm the p...

A: Let the exponential law of growth: As given: t=13.28 hours hence at night around 1:28 a.m., the de...

Q: A body moves on a coordinate line such that it has a position s= f(t) = ? - 7t + 6 on the interval 0...

A: Given , S =f(t)=t2-7t+6 and interval 0≤t≤6 Formula: Average velocity =[ f(b)-f(a)]/(b-a)

Q: A. f (t) = So sin(t - T) cos(7)dT

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Q: (x )dv, using simple substitution dv=f(x)dx_ Determine the value of f(x) if To evaluate the integral...

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Q: Find values of C1 and C2 so that the given functions will satisfy the prescribed initial conditions ...

A: A detailed solution is given below.

Q: To evaluate / (3x2+ 1) In x dx using integration by parts, it is best to let A u= 3x2; dv= In x dx B...

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Q: 3x2 sin? x dx

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Q: Look for three (3) mathematical formulas related to your chosen field like engineering, health scien...

A: Formula 1: y=mx+b y=mx+b  is slope intercept form equation of straight line. So it is used for findi...

Q: F. Planes and Lines O Find an equatin The plane each of whose paints idistant to The agu w eq point ...

A: Here ,              We have given two points which are               equidistant from each points of...