-+inf In(tan¯1x) 1+x2 1

Q: Determine if the two given converges or diverges. { п n 2n + - 1/ n=1 Σ n n \2n + 1 n=1

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Q: Q2) Solve the D.E xdy + (2y – xª + 3x)dx = 0

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Q: Find and dx d²y then simplify whenever possible. dx2 1) y = 3t5 – 2t , x= 4t³ |

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: If u + v + w = 0 and Ju = 3, |v = 5, |w| = 7 then the angle between u and v is O 21 3 O 5n 3 O None…

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Q: 7. Find the area of the region that lies inside the curve r = 3cos0 and outside r = 1+ cos0. Show…

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Q: If substitution technique is used to solve the integral |(12x+3x*)(10x² +x° – 2)´ dx then the -…

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Q: х2 — х — 2 lim х-2 х2 + х — 6 1. О 1 2. О 4/5 3. О 3/5 4. О 2/5

A: To evaluate: limx→2 x2-x-2x2+x-6 First factorize the numerator and denominator

Q: What is the area enclosed by the curve r = 2 cos 30? Answer is in square units. Use two (2) decimal…

A: First draw the diagram then find the interval and last intergate it.

Q: (b) S 3x5V1 – 2x³dx -

A: Given,              ∫3x51-2x3dx

Q: If uxv=uxw, u÷0 then O None of the choices O v=w+ ku O u=v+ kw Ow=u+ kv

A: u x v = u x w v = w but u is any other value so  v = w + ku

Q: Find the area of the shaded region. y y= xV4 x y=0 2 y= 0 -2 SQuare units 21

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Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 7z + 13 =…

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Q: b) (-1)"3n² 4n²–1 n=1

A: We will use root test.

Q: A thermometer is removed from hot water at 100° C into a room at 20° C. The temperature difference D…

A: Answer should be 20.254°C.

Q: I 3n O The region bounded by y = sin x and x- axis on the interval [-

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Q: [ 3x3-2х2-4х-3 х2 (х2+x+1)

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Q: dx 3 x² (9x²-4) 7

A: We have to use properties of integration to solve the question

Q: Using Lagrange multipliers, find three positive numbers whose sum is 6 and such that the sum of…

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Q: Which of the following vectors are not linearly independent? 日L O B O A

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Q: f(x) = x²+2x+1 g(x)= x+3 Set up the integral to find the area between the two curves. 1 -3 -2 -1

A: We have to find area bounded by the given curve.

Q: dy Find dz and simplify: y = 2534x²

A: we have to find derivative of the given function.

Q: If f(x)=sin(sin x) then f'(0) is .. Jika f(x)=sin(sin x) maka f'(0) adalah ... 1. O -1 2. O 1 3. O 0…

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Q: A true statement for the function f(x)=1/x is... 1. O f has an extreme value at the point infinite.…

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Q: Evaluate the integral ſ xe²" dx; * dx; u=x, dv= e²ª dx using integration by parts with the indicated…

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Q: (x² + 2x) cos(2x) d»

A: Given problem:- ∫ (x2 +2x)cos(2x) dx

Q: Find an equation of the line that is tangent to the graph of f and parallel to the given line.…

A: Given problem:- f(x) =x2 ,  Find equation of tangent line which parallel to line 8x-y+16=0

Q: +00 (-1)" cos(g) = >. g²n for all g e R (2n)! n=0 Calculate by using the 4th degree of Maclaurin…

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Q: 1 III. Consider an 1 for n eN = {1, 2, 3, ...}. 2n + 1 2n + 3 Find a general formula for the kth…

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Q: f(x) = -x^2 + x + 20 and g(x) = x^2 - 5x . Compute the area of the region enclosed  by the graphs of…

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Q: I. Evaluate the following integrals. 1. / 20- dx 2 x)5/2" x(9 – In².

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Q: 3. 6x° cos (x*) dx

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Q: Determine the third degree Maclaurin polynomial of f(x) = tan 3x. Use this to approximate the…

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Q: Determine the sum of the following series. (– 4)" -1 6" n=1

A: To find the sum of ∑n=1∞ -4n-16n   ∑n=1∞ -4n-16n = -41-161+-42-162+-43-163+-44-164+....⇒∑n=1∞…

Q: Solve for the following integral: 1 -dx (e2x – 4)5/2

A: I=∫1(e2x-4)52  dxu=-2xdx=-12 duI=-12 ∫due-u-452v=e-u −4dv=-e-u du-dv(v+4)=duI=12∫1v52 (v+4) dv

Q: +oo (-1)"n" sin" () ' Σ 2n n=1

A: According to question,Given series,∑n=1+∞-1nnnsinn1n2n

Q: Determine if the improper integral dx converges or diverges. - If it converges, find its value.

A: To determine whether the given integral converges or diverges.

Q: ********** . ...... Analyze and sketch a graph of the function. Find any intercepts, relative…

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Q: ´ax²-3 -, x > 1 х-1 Value of a and b that will make f (x) = continuous everywhere are .. (bx +2,x <…

A: To find the values of a and b that will make the function continuous everywhere.

Q: I. Evaluate the following integrals. •ln 2 #3. e2" sec-(e")dx

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Q: Find Duf at P. f (x, y) = 3(4 +xy)2; P(4,3); u = 1 i+ j NOTE: Enter the exact answer. Duf

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Q: x3 + 4x2 - 2 dx Ix? (x² + 2x + 2)

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Q: Determine the third degree Maclaurin polynomial of f(x) = tan 3x. Use this to approximate the…

A: The given function is; f(x)=tan(3x).

Q: 2. Find dy/dx: a. 3x? – (xy²)½ = 2y³ b. у%3D (сosx — ях)4x*

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Q: Find y' if 3x2- (ry?) = 2y.

A: y' = ? 3x2 -(xy2)1/2 = 2y3 3x2 - x1/2y = 2y3 differentiate with respect to x 6x - y/2x - xdy/dx =…

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j…

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Q: IV. Determine if the given is convergent or divergent. n Σ #2. (n² + 1)2 n=1

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Q: ¥2/3 6. cos'x sin x dx 5.

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Q: If sin theta is square root of (x^2 - 4), what is sin 2 theta?

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Q: Consider the following function. f(x) = x sin(x), a = 0, n = 4, -0.6 s x S 06 (a) Approximate f by a…

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Q: -1 4 1). -dx = -3

A: