Q1) Solve given differential equation using a variation of parameter method y" – y = 212 – t- 3

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A: Given that: Percentage of physicians, P(t)=100(1-e-0.42t)

Q: Find x²z ds, where C is the line segment from (0,6,4) to (1,3,-2) C

A:   ∫C y ds,  C: x=t2, y=t,  -2≤t≤3   dxdt = 2t,   dydt= 1∫Cy ds = ∫-23 t  (2t)2+1 dt=∫-23 t  4t2+1 dt...

Q: ydx + x(Inx - Iny - 1) dy = 0, when x = 1, y = e %3D %3D sin6o V. -5 A

A: Given:- ydx+x(lnx-lny-1) dy=0  To find :- Solution of given differential equation when x=1 , y=e

Q: 5. The differential equation (3r'e -21}dr +(r'e' -sin y Jdy = 0 is exact because ƏN %3D

A: Given:- Differential equation (3x2-2x) dx+(x3ey-siny)dy=0 To Find:- The given D.E is Exact because ∂...

Q: The partial fraction decomposition of 4x 12 can be written in the form of 8x2 + 30x + 7 g(x) f(æ) + ...

A: We have to find the value of f(x) and g(x) 

Q: Find the slope of the tangent line to the curve

A: Follow the procedure given below.

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A: Given that: y=ax2+bx+c passes through (1, 8) and tangent to line y=5x at origin.

Q: Find the dot product: (5, —3) о (2, 3) O 1 O -1

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Q: 1. What is the instantaneous slope of y = 5 at x = 5?

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Q: Determine if the given function is continuous and differentiable at the indicated values of x. Write...

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Q: 3. y = V(2x +5)3

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Q: 6. Verify the identity: sin x 1 + cosx 1 + cosx sin x 2 cscx %3D

A: Topic = Trigonometry

Q: Four friends plan to meet at the top of the Eiffel Tower. Each arrives about the time the tower open...

A: topic - solution of linear equations

Q: Let {xn} be a bounded sequence on R. Show that Xn lim = 0. - n→+∞ n

A: follow next step

Q: Question 3 Use the method of Lagrange multipliers to find the minimum of f (x, y) = xy? subject to t...

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Q: 3. lim Jx| ズート-1

A: Let's find. 

Q: (x+1)dy = (2xe* - xy – 2y)dx

A: Solved below

Q: Between 2006 and 2016, the number of applications for patents, N, grew by about 4.9% per year. That ...

A: Given: N'(t)=0.049 N(t)Therefore:dNdt=0.049 N

Q: Let ū = (1,0, 2), ū = (0, –3, 5). Find the projection of i onto ū.

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Q: B. Determine if lim f (x) = f (c)

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Q: Which of the following uses integration by parts? (1) fxcosx'dx (3) fxlnx Inx d (2) fxe"dx (4) A (2)...

A: We have to find out

Q: The partial fraction decomposition of 4x2 x + 7 can be written in the x3 + 4x2 + 9x + 36 f(x) g(x) +...

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Q: 1. The differential equation (3x +2xy +4y dx+(r' +8ry +18ydy = 0 is exact because %3D OM ON

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Q: Find the value of 6dx x2 + 1 1 Determine whether 6 n² + 1 n=1 is a convergent series. Enter C if ser...

A: Given query is to find the value of the integral.

Q: What is the Order of the equation? O 1 O 2 O 2/3 Оз What is the DEGREE of the equation?

A: Follow the procedure given below.

Q: y = C1e2 + C2e- y' +y – 2y = 0 y" + y + 2y = 0 O Option 3 O option 1 y" – y +2y = 0 %3D

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Q: Find the projected value of the function.

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Q: Determine C when x=y=0 (xy+ 2)dx = (x'y +x² + y? + (z²y + z? + y} +1) dy %3D

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Q: Find the area of the region bounded by: r 72 cos 20

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Q: 5.2.1. Evaluate the Frobenius matrix norm for each matrix below. (0 1 0 B= |0 0 1 1 0 4 -2 4. A= (3)...

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Q: Find the maximum rate of change of f(x, y, z) = x + y/z at the point (1, 1, -5) and the direction in...

A: We have to find the maximum rate of change

Q: Which of the following differential equations can be classified as separable and exact?

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Q: Whet is the particular solution if y(1)-07 zy = y+ (x² + y²)² y =z sin (In z) Arcsin 2- - In z + 1 O...

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Q: Perform the indicated integrations. 1. S- ydy 25-16y 2. zdx 9+x2 dx 3. Jax-4x+5

A: since you have posted multiple question i can do first three question as per our company guidelines....

Q: The demand function for a company's product is p = 24e-0.39 where g is measured in thousands of unit...

A: Given query is to find cost per unit for the first part and the unit sold for the second part.

Q: 3. S (x + ) dx

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Q: Let а 3 (1,0, —2). 6 = (3, 1, –1). č = (1,0, –1). - Find the triple scalar product ā o (b × č), and ...

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Q: a) Find the population after 7 years. (Round to the nearest integer as nee

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Q: The integral expression J 2x sec( 5x) tan (5x) dx can be evaluated using integration by parts of the...

A: Given that: ∫2xsec(5x)tan(5x)dx

Q: hCt)-5t (1-ビ ((チ1) (け)

A: Given query is to find the derivative of the expression using product rule.

Q: cost C (in dollars) of manufacturing ¤ number of high-quality computer laser printers is C(x) = 9x*/...

A: Given query is to find the rate of change of cost.

Q: Calculate a double integral of the figure, where R is the region bounded by y = x2 and y=2x. The ans...

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Q: h (x)= 3

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Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -...

A: The height of the ball f(t)=-16t2+326t+22

Q: Determine whether each of the following functions is (a) continuous (b) differentiable 1. f(x) = x2 ...

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Q: (1+y² ;+ cosx – 2xy) y' = yly + sinx] ;when x = 0, y = 1 %3D

A: NOTE: Refresh your page if you can't see any equations. .

Q: Determine the order and degree of the following equations: a.) (d^2y/dx^2)^2 = (dy/dx+4)^3/2 b.) sqr...

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Q: Find the limit. Enter DNE if the limit does not exist. lim (z,y) → (0,0) ² + 15y²

A: Here we will solve the given limit,

Q: Solve the following problems below about derivative. Simplify your answers if necessary. 1. A three-...

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Q: Find the volume of the solid bounded by the paraboloid z=2 +x2 + (y - 2)2 and the planes z=1, x= -1,...

A: We are asked to find the volume.