Consider the equation ay" + 4y' + cy = 0 the constants a,c,m are real and different from zero, the general solution has the following form: y(x) = C,emz + C,xe™z %3D We can affirm that: О a) ас > 16 O b) ac = 16 %3D О d) ас > 4

Q: Evaluate the double integral over the rectangular region R. / 8xy°dA; R = {(x, y): – 1 < x < 1, – 7…

A: Given:       ∬R8xy6dA   R=x,y: -1≤x≤1 , -7≤y≤7        ∬Rfx,ydA=∫ab∫cdfx,ydydx…

Q: Evaluate the double integral f(r, 0) dA. -7 cos(0) r dr de 497 2 Sketch the region R. 7/2 A/2 6 2 4…

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Q: Find T(t) and N(t) at the given point. r(t) = 3 cos(t)i + 3 sin(t)j + tk; t= 2

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Q: Problem 5 Find the Maclaurin series for f(x) and its associated radius of convergence. (a) f(x) =…

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Q: r=1+ 3sino

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Q: please

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Q: - x)dx 1 X 2 х +x+1

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Q: Consider the following planes. 5x + 2y – z =22 X- 4y + 2z = 0 (a) Find the angle between the two…

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Q: Determine the area of the region enclosed by y3x^2 and y=x^1/2

A: To find the area of the region enclosed by the given curves.

Q: Use a double integral to find the volume under the plane z = 22x + yand over the rectangle R = {(x,…

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Q: Find the divergence of F(x, y, z) =(a -1 Y, y? + 1' 3xz2 + 2y ) at (2,0, – x COS

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Q: Example 6 Video Example 0 A particle moves along a line so that its velocity at time t is v(t) = t2…

A: Given;  v(t)=t2-t-12.

Q: Evaluate the triple integral. xy sin(yz) dV, where G is the rectangular box defined by the…

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Q: Use the arc length formula to find the length of the curve y = 3x - 5, -2 SxS 3. Check your answer…

A: This question is related to Functions and curves, we will solve it using given information.

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. V64-22 xy dy dx dz

A: Given: I=∫08∫064-z2∫0xxydydxdz   The Power rule: ∫xndx=xn+1n+1+C

Q: dx a sin x+b cos x

A: Given problem:-

Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

A: To find maxima/minima of the function: f(x,y)=x2+2y2-3xy with constraint g(x,y)=x+y-24=0

Q: Use the arc length formula to find the length of the curve  y = 3x − 5,   −2 ≤ x ≤ 3.  Check your…

A: Given : y=3x-5 ,   -2≤x≤3   To Find : Arc length

Q: h sin 2 xdx X COs 2

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Q: Question 14 Find the area of the surface that is generated by revolving the portion of the curve y=…

A: Given: y=x2⇒x= ±y Since , we are dealing with x=1 to x=2, we will take the positive value Thus, x=y…

Q: k lim (1+†) k→∞ k

A: We have to find limit

Q: 2. Determine whether the statement is True or False. If it is false, explain what makes it false, or…

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Q: FOTE: Enter the exact answer. dx dy = VT

A: A detailed solution is given below.

Q: Find the distance of the centerof gravity of the area on the first quadrant region bounded by the…

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Q: 1. Sket dh the graph of the cylinder r = (y – 2)2 in R. %3D

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Q: = -8i+ (1 – tj+tk O It is a parabola in the plane x = -8, with vertex at (-8, 1, 0), opening to the…

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Q: Question 9 1/2 Evaluate the iterated integrals J. J. sine r cos e dr de A 1/6 B) 1/2 6 D) 11/9

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Q: 1- Show that the following subset is a subgroup. H = {o e S, l0(n) = n}cS,

A: We have to show given subset is a subgroup.

Q: Find f such that the given conditions are satisfied. 17) f(x) = 5x2 - 7x + 4, f(0) = 2 A) f(x) =x3…

A: Given f'(x)=5x2-7x+4,   f(0)=2To find f:

Q: Find the area of the region outside the cardioid r = 4 – 4 cos 0 and inside the circle r = 8. NOTE:…

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Q: What is the period and domain of the basic tangent function y=tan(x)? @ *E, 2n, {x€R|x= (2k + 1)m…

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Q: Set up a triple integral for the volume of the solid. Do not evaluate the integral. The solid…

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Q: A shelter rescues 4 cats for every 5 dogs. If they rescued 48 cats how many dogs did they rescue?

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Q: 1-sin8 Evaluate the iterated integrals r2 cose dr de A 1 B) 2 D) 3

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

A: Solution is done in step 2

Q: xydA R

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Q: What is the closed-form expression for the series 2 (k+ 1)², k=1 13 n3 + B

A: First expand the squre  term and make it in standard format then use the formula of summation.

Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating d dt dt the product directly…

A: r1(t)=cost i+sint j +3t kdr1dt=-sint i+ cost j+3 kr2(t)=2i +t kdr2dt=k

Q: loge (cos x) e. lim x V1+x2 -1

A: e.limx→0logecosx1+x2-1

Q: Find the area of the shaded region. r = Vcos 20 r = 14 cos 0 NOTE: Enter the exact answer. A =

A: Area of shaded region .

Q: Use a triple integral to find the volume of the given solid. The solid bounded by the parabolic…

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Q: Calculate the derivative of 2t – 1 > t + 2 r(t) =< 3t – 5, 2t2 + 5t + 7,

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Q: Question Specify which of the following sequences converge en n+V5 an =5- %3D n2 Cn = an and Cn the…

A: If limn→∞an  exists and is finite the then sequence an is converges.

Q: Evaluate the iterated integral. 1 z y SS§ 9ze=v² dr dy dz

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Q: A torus is formed by revolving the region bounded by the circle x? + y? = 49 about the line x = 8…

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Q: Question 15 1-sine Evaluate the iterated integrals J. J. p2 cose dr de̟ A 1 В) 2

A: ddθ(sinθ)=cosθ ∫rndr=rn+1n+1, for any real number n.

Q: We know that y dy? arctan (e*+1) so whats the value for dx 1 a) e2a+2 +1 1 Ob) els+1)* +1 Need This…

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Q: Use a double integral in polar coordinates to find the volume V of the solid bounded by the graphs…

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Q: Find the area of the region(s) enclosed by the curve y= |2x-6|, the x-axis, and the lines x =0 and x…

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Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: We have to find the volume by shell method.