A. Find the area of the plane region bounded by the given curves 1. y = x, y = 2x, and x +y = 6 (Answer: 3 s. u.)

Q: Evaluate the double integral over the given region. 9x sin xy dA, R: OSXST, Osy<1 R

A:

Q: 4 Which formula would be used to calculate the trapezoid approximation of L dx using five…

A: We have to use trapezoidal rule. Option B is correct.

Q: Find the Taylor polynomial of order 3 generated by f at a. f(x) = x2 + x+ 1, a= 7

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Q: -2 Sx'V4 – x²dx

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Q: 9х1 +5х* +2 3x- 3х-2

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Q: Solve the equation on the interval 0s0<2r. cot 0+ 3 =0

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Q: Find the total differential dw. 4. w = e*" – sin(yz) -

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Q: Find a power series representation for f (t) = ln(10 – t). %3D

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Q: Solve the following initial value problem. f′′(x)=−36x^2−18x−4,f′(−1)=13,f(−1)=−35

A: To solve the initial value problem.

Q: dy for xy +e* = sin(x+1). By using implicit differentiation, find dxx.y)-(1.0)

A: Given equation: xy+ex2y=sin⁡(x+1) To find: dydx(x,y)=(1,0)

Q: A 15-foot ladder is leaning against a wall. If we pull the ladder away from the wall at a rate of…

A:

Q: 2у — 4 dy 2 + 49 с.

A: To evaluate: I=∫2y-4y2y+2dy=-∫4y-2y2y+2dy=-∫22y-2y2y+2dy=-∫2y-12y+22ydy=-1ln 2∫2y-12y+22yln 2dy

Q: Find the area A of the sector shown in each figure. (a) 72° 4 A = (b) 0.5 rad 16 A=

A:

Q: b. dx Vr - 2x2 + 1

A: To evaluate: I=∫x5x4-2x2+13dx=12∫x22(x2)2-2x2+132xdx Substitute x2=u⇒2xdx=du

Q: The focus of the parabola defined by the equation x2 = 20 y is (4, 5) (0, 0) Option 1 Option 2 (0,…

A: Given query is to find the focus of the parabola.

Q: The power series representation of 1 f (x) = 5x + 4 is: 5 25 125 x+... 256 | - 4 16 64 125 x+... 256…

A: In this question we have to find series form of the function.

Q: 2x J(x – 3)2 A = 6, B = 2 A = 2, B = 6 A = 2, B = - 6 A = - 2, B = - 6 A = - 2,B = 6 None of the…

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Q: 2 5. Given cos a =- and tan ß =- 2 575BS7, determine the exact COs a value of: a) cos(a + B) and b)…

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Q: 5. w = x tan-y - 2=

A: Given: w=xtan-1y-2xyz

Q: Given : v = (3t – x)e-2t Find atəx

A:

Q: In a race, Anita Hurrie walks 100 m due east and then walks N70 E for 60 m. How far is Anita from…

A: First draw the diagram then make a vector ..and then find the magnitude of this vector. And use the…

Q: iv. L, x* (e* – e*) dx

A: Given:

Q: Evauate: |(*+xy) dx+ Cy- xy)dy; C: the x-axis from the origin to 2,0) and then line x-2 from (2,07…

A:

Q: sin(x²) 1+0- e2r – 2x – 1° Evaluate lim

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

Q: Evaluate the following integrals. (csc 0)(1+ sin? 0 + sin 0 cot? 0) de a.

A: This question is based on indefinite integral.

Q: a. (csc 0)(1+ sin² 0 + sin 0 cot? 0) d0 5.

A: We will solve the integration

Q: 20. tan (20) = -1 %3D

A: We have to find the value of θ.

Q: .C find the firet order parhal dervohve f 4.5 1. z) = e 32 W="y - 10y2³ + 432 hCs, t) =° t?In ts) +…

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Q: 15. Determine the coordinate of point C, which lies on the y-axis, if it is equidistant from point A…

A:

Q: Let p(x) be a polynomial of degree 3. Its derivatives, around the point æ = -5, are as follows:…

A: solution:-let p(x) be a polynomial of degree 3p(x)=ax3+bx2+cx+dwhere a,b,c &amp; d are parametersat…

Q: What is the volume of the solid generated by revolving about the x-axis, the region bounded by y =…

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Q: 4. y = x, y = 2x, and x + y = 6 (Answer: 3 s. u.)

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Q: What are the direction numbers of a line given by the parametric equation:  x=6+t,y=5+4t,z=1−2t

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Q: II. Find the Inverse Laplace of the following 2s-9 d. s2 +2 1 е. (s²+1)(s²+4s+8)

A: We have to find the inverse laplace transform.

Q: What are the two values of k closest to - 4 for which S, sin? (x + 4) – cos2 (x + 4) dx has a value…

A:

Q: Find and sketch the domain for the function. foxy) = - 25) ( - 4) Find the domain of the function.…

A: function f(x,y)=(x2-25)(y2-4)

Q: Q7: Í sin(3z)cos(4z) dz = a)cos z- cos(72) + C b) -tcus x -os(Ix) + C %3D Qe S sin'x cas d = 2).

A:

Q: 2. If the acceleration function of a certain particle is given by a(t) the velocity function…

A: We know that if we integrate the acceleration function then we get the velocity function . we used…

Q: 00 Write the Taylor series for f(x) = e* about x = Σ- 3)". 3 as n=0 Find the first five…

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Q: Using Laplace transform to solve the IVP: y" – 9y = e *, y(0) = 0, /(0) = 0 %3D we find the solution…

A: The given IVP is y''-9y =e-3t,   y(0) =0, y'(0) =0 To solve the problem we must know the following…

Q: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…

A: Given problem:- Use Intermediate Value Theorem to explain why the function has a zero in the given…

Q: 6n + 2 6n+2 Let > and an 5" 5" n=1 an+1 a) Find lim n-0 an 6n+2 b) Determine whether 2 is convergent…

A: Convergence of series.

Q: Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as…

A: We have to simplify

Q: Find the slopes of the surface at the given point in the x-direction and the y-direction. z = x2 -…

A: This question is related to slope of surfaces, we will solve it using given information.

Q: Find the derivative of the function at Po in the direction of A. f(x,y.z) = xy+yz+ zx, Po(-1,1,2).…

A: Given :f(x,y,z)=xy+yz+zx

Q: On what interval(s) is f'(x) increasing? Decreasing? Explain.

A:

Q: Two lines have equations L1: (0,0,1) + s(1,-1,1), s e R and L,: (2,1,3) + (2, 1,0), e R. 10. What is…

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Q: Given the slope field below, which function describes the given graph. A. y' = x? + y +1 B. y' = x*…

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Q: explain

A: We will check whether fundamental theorem of calculus applies.

Q: n3 + n? ) Σ 00 (n – 1)! n=1 2n + 3 n2 In n n=1

A: