Given the combined differential operators for a given differential equation (D + 7)³ (D – 2)(D + 1) Determine the general solution to the differential equation. = A cos(7 x) + B sin ( /7 x) A B = A x-7 + B x² + C x-! y(x) = – 7x + Be2* + C e-x A e y(x) = Ax? e7* + Bx e7* + C e7* + De-2* + Eе^ y(x) = Ax² e-7x + Bx e-7x – 7x + De2* + E e-x + Се y(x) = Ax² cos(/7 x) + Bx cos(/7x) + C cos(vīx) + Dx² sin( /7 x) + Ex sin( /7x) + F sin(/7x) + G e²«. + He-* y(x) = Ax e + B e™* + C e-2 + D e* H y(x) = Ax e –7x + Ве + D e¯*

Q: the given point Find the gradient of the Function at 3x² -5y2 + 2z² (1,!,-2) %3D

A:

Q: Evaluate: / tan( tan3x)dr cos?3x i -In |sec(tan3x)|+C A 3 В - In |cos(tan3x)|+C -In |sin(tan3x)|+C 3...

A:

Q: 27 for fC ), Obtain Fourier series of period where flx) = メ -下SYくO oく*くて

A:

Q: Find the arc length of the curve x = –3y3/2 from y = 0 to y = 10. Length =

A: To find the arc-length if the curve x=-3y32 from y=0 to y=10 Now, the formula for the arc-length is:...

Q: There are some sweets in a container. When the sweets are put into bags of 4 or 10, there are no swe...

A: topic - lowest common multiple

Q: 7–√7

A:

Q: k! CO %3D 104k

A: Given Series ∑k=0∞k!104k

Q: Let s(t) = 6t – 27t² – 180t be the equation of motion for a particle. Find a function for the veloci...

A: We need to find velocity and acceleration function.

Q: Use the total differential to approximate the quantity. Then use a calculator to approximate the qua...

A:

Q: Function f(x, y) = 7x – 8y + 2xy – x² + y° -

A: we need to find the extreme points of f(x,y)=7x-8y+2xy-x2+y3  

Q: У(xtanx + Inу)dx + tanxdy 3D C

A: The given equation is; y(tan x+ln x)dx+tan xdy=0

Q: Solve for t e2t+ 4et + 4= 0 e2−4t + 5 = 20

A:

Q: Calculate the Taylor polynomials T;(x) and T3(x) centered at a = 8 for f(x) = In(x + 1).

A:

Q: Evaluate. x - 1 dx 9 x + Va if b > 4, find b² + 36 +5

A:

Q: csc5x cot5x dx A csc5x B esc5x 3 -csc5x 3 D csc5x E) None

A: Given  ∫csc5x cot5x dx5csc5x3    

Q: (a) D = (x + z)a, (b) E = (y² – x³)a, + xyza, + (x² – z?)a.

A:

Q: csc5x cot5x dx 5csc5x (A csc5x B csc 1 -csc5x 3 В 1 -csc5x 3 D csc5x None

A:

Q: S e3(2e * – 1 ) dx (ear – 2) (e3* + 1) 4 (A) 2e3x – 1 B) 2e 6r – e 3x © (e3r – 2)+ D (e*+1)+ (E ,6x ...

A:

Q: Use the Integral Test to determine if the series shown below converges or diverges. Be sure to check...

A: If integral value is finite then given series is convergent. 

Q: 5. Find lim f(x) f(x) 2 1 i -1 2 -2

A:

Q: tan(tan 3x)dx cos? 3xl

A:

Q: Use traces to graph and name the surface

A: The given surface is: x24-y29+z216=1...(1)

Q: |(9 cos(9 x) +4 sin(4 x))dx =sin(9x)-cos(4x) +c Select one: True O False

A: topic- indefinite integral

Q: Integration is the reverse process of differentiation.

A: Given,            Integration is the reverse process of differentiation.To find : State true or fals...

Q: 1. Write the improper integral which is represented by the following limit. lim C2" 2x dx x2-4 2. Sh...

A:

Q: e Does the series E converge or diverge? 8n n=1 1+ e

A:

Q: Compute the surface area of the solid of revolution formed by rotating the bounded region formed fro...

A:

Q: 4 Find the area bounded by Y 0, y = 0, x = 2. %3D /144 – 16x? Round to four decimal places.

A: We have to use definite integration. 

Q: e(2e" – 1)dx 6x 3x A 2e - 1 B 2e 6i – e 3u © (e"-2)+ (e" + 1)4 E F None

A: This is a problem of integration. First here we will assume e^3x = t and then we will use general fo...

Q: range of the function. (a) If f(x) = 3x + 4, find the image of 4. (b) If f(x) = 7x + 5, find the ima...

A:

Q: Q4: Find the following limits if exist:-- x-1 x2-x 1) limx-1²+2x-3 2) limx-1 x²+3-2

A:

Q: Question Select your answer. On which interval(s) is ƒ(x) = 2 ln(x² +x – 20) continuous? (-00, –5) (...

A: Topic:- calculus  Note :- as per our guideline if more than one question uploaded than only first qu...

Q: y' + 2xy = 0

A: y'+2xy=0

Q: Given the function f(x) = x?e%z, Determine the open interval(s) where the function is concave up Det...

A:

Q: xydy – (y² + 3x²)dx = 0

A: Let, y =v*x

Q: Find a formula for the nth partial sum of the series and use it to determine if the series converges...

A:

Q: Consider the series (-1)"(2x+ 3)". n=0 (a) Find the series' radius and interval of convergence. (b) ...

A:

Q: 5. Discuss real world quantities that the circulation of a vector field around a closed loop could m...

A:

Q: Evaluate the improper integral or state that it is divergent. (Hint: change to limit then factor the...

A:

Q: (a) f(x) is shifted 5 units upward. y = (b) f(x) is shifted 6 units to the right. y = (c) f(x) is re...

A:

Q: tion f(x) = x cosx.

A:

Q: Integration using Partial Fraction! dx X(x²

A:

Q: the following ordinary different is nonlinear? = of them (4) – 2y = 2x – 3y u(4) – x³ y" – 2y' = 2x ...

A: We have to choose the correct option according to the given information

Q: Estimate the area of the curve y= from r = 0 to r = 3 by using 6 rectangles and right end-points, R6...

A: area and right end sum

Q: Below is the function f(x). 7+ -7 -6 -5 -4 -3 -2 1 4 -4 -5 -6 Over which interval of æ values is f' ...

A: This question is based on derivative application of function.

Q: Q3:A| Prove that:- cos x 1) 1+sin x 1+sin x = 2 sec x cos x tan? x 2) tan? x+1 = sin x

A: topic - trigonometric identities

Q: D+ E(x – 2) + F(x – 2)² + G(æ – 2)³ -

A:

Q: 2 3 2 Q5. Evaluate the value of integral |[xy'z dx dy dz . 0 11

A: I have stated the used formula in the solution

Q: Find the shortest distance from the point (2,0,–3) to the plane x +y + z = 1.

A:

Q: Question 4 (sin(3t))^2(cos31)) dt

A: To evaluate the integral ∫sin23tcos3tdt Formula used: Power rule of differentiation ∫xndx=xn+1n+1+c ...