Evaluate the expression. 12 O A. 66 О в. 6 О с. 33 O D. 239,500,800

Q: Find the particular solution of the DE y " -11y + 24y = 0 subject to the boundary conditions y (0) =…

A: Given y''-11y'+24y=0  ; y(0)=2  and  y'(0)=-3

Q: b. Vr4 – 2.x² + 1 dx

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Q: The following telescoping series 00 1 Σ- en+1 – en+2 n=1 converges to Ve the above none of them…

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Q: Using appropriate substitution 1 dx V9x² – 36x + 37 Is equal to

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Q: Solve for the derivative of the following composite functions. f(g(x)) = (x+ 4)* 2 f(9(x)) = (2x2 +…

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Q: 2. lim (ex – 1)lnx X0+

A: (2). The given limit is: limx→0+ex-1lnx As we know that, the second indeterminate form is: ±∞±∞ ;…

Q: Q1: Find the length of a and b in the following triangle a 75 30

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Q: Question 5 Find the volume of the solid that results when the region enclosed by the given curves is…

A: To find the volume of the solid that results when the region enclosed by the given curves is…

Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

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Q: Solve the differential equation Integrating Factor by Linear Equation: (xy² + x²)dy + xydx = 0 %3D

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Q: 1. Maximizing. Determine the region R in the xy-plane that maximizes the value of SR S(9 – a2 –…

A: To determine the range .

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabolic arc y = x² from (0,0) to…

A: For the arc y = x2 and the range of x from 0 to 1. So, dy = 2x dx. Now,…

Q: 1.) ° 6x3+4x²-8x dx I. Evaluate the following Definite Integral. 1.) ° 6x³+4x²-8x 2.) x²(2x3 + 1)Fdx…

A: we want to find the integral ∫03( 3x-6 -1 )  dx

Q: for x[z] given by z1 x[z]: 1-z2 then X[00] equal to Select one: a. 0.5 b. 0

A: B is the correct option.

Q: Find div F and curl F if F(x, y, z) = x*i – 5j + yzk. - div F= curl F=

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Q: 2. Determine the area of the region bounded by the curve y = x3 – x2 – 2x, and а. the x-axis

A: Given:    a)   Curve y=x3-x2-2x Curve cuts the x-axis at           x3-x2-2x=0           xx2-x-2=0…

Q: 5. y!! + 2y! +v = 7+75sin2x

A:

Q: 129, given 18) Find y'= A) 2y/(2x - sin y) C) - 2x/(2y - cos y) in terms of x and y for an Implicit…

A: Given; y^2+x^2=siny+4

Q: Evaluate the surface integral. /| xz ds, S is the part of the plane 2x + 2y + z= 4 that lies in the…

A: We need to find surface integral.

Q: Barbara put P100 into banks savings account. The account accrues a 9% interest rate compounded…

A: Given: Amount =P100 . Rate of interest= 9%  Time n= 12 years

Q: 33) In Problems 33) through 35), given MB ' (x) = HD(x), HD' (x) = PR (x) , PR' (x) = RB(x) with the…

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Q: Find the area of the inner loop of the curve r= 1-2cos θ

A: For the inner loop of the curve 1-2cos θ=0⇒2cos θ=1⇒cos θ=12⇒θ=cos-112⇒θ=π3,5π3

Q: Using appropriate substitution X dx (x + 1)² 4 is equal to V4- (x+ 1)? -sin-) +C none of them the…

A: this is a problem of integration. Based on the proper substitution and formula we will answer the…

Q: Using Sandwich Theorem 3n? + 1 an = (-1)" n3 – 4 converges to 1 diverges converges to -1 none of…

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Q: Using Long (Euclidean) division then decomposition into partial fractions x4 – 4x2 – x – 3 | dx х2 —…

A: We have to find value of given indefinite Integration.

Q: dy For each of the following functions determine da

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Q: the 6) Find the a by curves y=x° and y=X ea of the region enclosed A) D)

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Q: Find the radius of convergence, R, of the series. xn + 1 3n! n = 2 R = Find the interval, I, of…

A: A detailed solution is given below.

Q: 3.) ž sin'(x)dx

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Q: Q4: Find the corresponding Spherical polar coordinates of the Cartesian coordinates (6,2,5).

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Q: d 5x+3 4. dx 7x+2

A: As we know that; The Power law: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2 And c·f'=c·f' ; where…

Q: Hello, may I ask how was this part obtained? Why are there A and B? This part wasn't on our lesson…

A: This part: 4v+24v-1v+2=A4v-1+Bv+2 is called partial fraction decomposition. Using this we make two…

Q: 2) 2x2 csck) dy d X M) y'= Xe'Vx-2

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Q: 3. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1…

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Q: 7. lim vx2 + x + 1 – Vx2 + 1

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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 9x from (9, 9) to (0,0). NOTE: Enter…

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Q: Find div F and curl F if F(x, y, z) = 17y®z*i – 8x'z®j – 4cy°k. %3D - div F= curl F=

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Q: 5. Given the General Solution the DE, Identify the roots * y = C1e¬2x + C2cos2x + C3sin2x O A) m1=…

A: Here, the solution to the DE is: y=C1e-2x+C2cos 2x+C3sin 2x...(1)

Q: cx2 + 8x if x < 3 Let f(x) = 1 x3- cx if x 2 3. For what value of the constant c is the function f…

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Q: x")' = a xa-,(x)'=1 and (constant )'= 0. %3D x+2 Using Quotient Rule (£)' = f'g-fg') x-1 A) 2x/…

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Q: ind the arc length oI the parametric curve. 0 = 6 cos (t), y = 6 sin(t), z = 8t; 0 stST

A: Given: x=6cost, y=6sint, z=8t

Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z = 4xe…

A: All four second derivative are evaluated.

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(1) = i – 26j + %3D (a) r(t) 3ti- 2j + 2 k (b)…

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Q: Find the integral | 2(x* – x°)(x5 – 1)®dx а. b. In x2 dx 2х J x + 3)* С. 5.

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Q: 1 Without a table of values and using index laws, sketch y 2*-

A: y=12x 2-1 y=12x2 y=22x

Q: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

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Q: Describe the graph of the equation. r = 7 sin 8t i – 7 cos 8t j It is a circle of radius 7 in the…

A: Explanation of the answer is as follows

Q: 5. y = (x+7)(5x- 2)

A: Given : y=(x+7)(5x-2)   To Find : Derivative of the given function.

Q: Evaluate the triple integral. Xyz dV, where G is the solid in the first octant that is bounded by…

A: Integral