1. Evaluate the following integrals. (a) r* log r dr

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Q: the following statements is IR

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Q: Find the general solution of the given differential equation. y dx - 5(x + y') dy = 0 x(y)

A: This is a problem related to differential equation. Based on the general formula we will answer the…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x2 - y2, (6, 3, 27)…

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Q: Evaluate the following integrals. x³ + 4x² – 2 dx x² (x² + 2x + 2)

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Q: 1 Let f (x,y)=In . Then f „(1, – 1) =...... 3x²+4y3 XX

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Q: Find the sum of the given convergent series. > [tan-1(2n – 1) – tan-1(2n + 3)] n=0

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Q: Exv3x² + 4 dx %3D 1 (3x² + 4)v3x² + 4 +c 3

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Q: 13 4. Consider the function f(x)% = for a 2 (a) Draw a graph of this function on the interval [0,…

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Q: Solve the following equation. (x – 4)2 – (x – 4) – 20 = 0 List your answers separated by a comma.…

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Q: Consider a triangle where A = 30°, a = 1.8 cm, and b = 1.3 cm. A C (Note that the triangle shown is…

A: topic - Law of sines

Q: sec (t) – 1 sec2 (t) Simplify to an expression involving a single trig function with no fractions.…

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Q: 3" en – 2n n=1

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Q: Find the surface area of the sphere x^2 + y^2 + z^2 = 100 that lies above the cone z = sqrt(x^2 +…

A: We need to find surface area.

Q: Consider the function f(x)=4x+1. (a) Estimate the area between the graph of f and the x-axis between…

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Q: Let A = (1,0, 2) and B = (6,-2,3). Solve for projĄB.

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: Question If 0 < 0 < 2n and 4sin 0 – 4 = -3, determine the values of 0. List your answers as exact…

A: Answer: The solution is as given below:

Q: 3. Find the value of c guaranteed by the MVT for integrals for f(x) = cos(x), [-; 3'3 ] over this…

A: f(x)= cosx  , [ -π3,π3]as per MVT for Integrals for a function f(x) bounded and integrable on [a,b],…

Q: 1. El radio de convergencia de la serie de potencias es (n+1)!

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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: Calculus question

A: Detailed explanation is attached.

Q: Find the area of the region bounded by the given curves. y = x², y = 4x – x² - ly=x²

A: We have to find area of bounded region.

Q: state whether Converges diverges

A: To state whether the given series converges/diverges. ∑n=1+∞-1nnnsinn1n2n

Q: Determine whether the following converges or diverges {(5) n 2n +1 n=1

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Q: If m < f(x) <M for a <x s b, where m is the absolute minimum andM is the absolute maximum of f on…

A: We need to find smaller and larger value.

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: Keith is flying two kites. He has 100 feet of string out to one kite and 110 feet out to the other…

A: From the given information, we have to find the distance between two kites.

Q: Find the general indefinite integral. (Use C for the constant of integration.) x3 + 12), 343 x*+C 2

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Q: Question Using Rolle's theorem for the following function, find all values c in the given interval…

A: f(x) =2x3+452x2+21x-2Since f(x) is a polynomialIt is continuous on -4,2It is differentiable on…

Q: 6. lim e (x, y)→(1, –1) cos(x + y) -xy

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Q: Determine the equation of the tangent line to the curve f(x) = 2sinx + sin²x at the point (E)

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Q: Consider replacing F by an alternative set of functional dependencies G: AP-> IT I -> ATP Is the…

A: answer is in next step

Q: 1 vn Vn + 1, n=16

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Q: Find the area ef"l fhe Shaded reghon a/2

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Show clear and detailed solutions. Given: Let A = (1,0, 2) and B = (6,–2, 3) Solve and calculate for…

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Q: 3. Find the exact length of the curve. Show All Work and Give Answer In Simplest Form. x =1+3t²,…

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Q: 2x3 – x² + 2x – 2 dx x²(x² – 2x + 2) - -

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Q: Use the indicated change of variables to evaluate the double integral. 4(x2 + y²) dA X = y = (0, 1)…

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Q: evaluate the function f(x)=−3x2+2x at the given input a) f (- 2 ) b) f (a)

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Q: Q5. Find if y = Vcos x - 7*

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Q: Given the following power series, use Alternating Series Test to prove that the series converges…

A: We have to check for x=11 given series is convergent.

Q: Find the standard form of the equation of the ellipse with the given characteristics. Center: (5,…

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Q: Find the most general antiderivative of the function. antiderivative.) g(u) = 6u + Vū

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Q: 273 - 22 + 2r – 2 dr 1²(r² – 2x + 2)

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Q: A radioactive substance decays according to A=A0e^−0.0048t, where A0 is the initial amount and t is…

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