Evaluate the definite integrals using properties of the definite integral and the fact that 5 5 S √³ f (x) dx = 10, and √²9 (x) dx = 3. 121(2) f(x) dx = -2,

Q: (a)Show that F is a conservative vector field. f(x,y,z) = (b)Find a potential function for F.

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Q: `11,  Find a function  f(n)  that identifies the nth term  an  of the recursively defined sequence,…

A: The solution is given below

Q: Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of…

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Q: 9. dt + 을 = COS t + Answer: s = sin t + 을..

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Q: I. Find the solution set of the following. 2. 3x²+2x³7x² - 4x +2=0

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Q: I. Find the solution set of the following. 2. 3x² + 2x³ — 7x² - 4x + 2 = 0

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Q: Consider the power series Σ#1 ¹+∞0 n(3x+2)n n=1 n³+4 1. Show that the series is absolutely…

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Q: Given R = = [² (³ + + ²) - (² + 4)] i n n a= So integral, that is provide a, b and f(x) in the…

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Q: The graph of a function is given. Determine the average rate of change of the function between the…

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Q: 4. Verify if the following equations general solution: are exact and find the 2 9. 2xydx + (1 + x²)…

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Q: [2 2x log 2x dx

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Q: Sketch the area bounded by x^2 + 2y = 4 and x + y + 2 = 0 on the image below and determine the…

A: volume of above function is π×175.19 cube unit

Q: Using the Factor Theorem, which polynomial function has the zeros 5 and 4-5/? Ox²-9x-5x + 25/+20…

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Q: Find the solution to ty""+612 y" +29ty-29y=0; y(1)=2, y'(1)=-3, y"(1)=19

A: The given equation is; t3y''' +6t2y'' +29ty' -29y=0, y(1)=2, y'(1)=-3, y''(1)=19.

Q: Suppose that h(x) = f(x) g(x) and that we know the following f'(3) = -1, g(3) = 2, & g'(3) = -5.…

A: Topic:- calculus

Q: What is the slope of a line that is perpendicular to y = 3x + 1? -1/3 -3 3 1/3

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Q: I. Find the solution set of the following. 1. 2e²3e + 1 = 0

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Q: Find the transfer function, G(s)=C(s)/R(s), corresponding to the differential equation, d³c dt3 +30²…

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Q: 1 S. cot ³ x dx

A: I have stated the used formulas in the solution

Q: the

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Q: 7. y - y = 16

A: The objective is to find the general solution .

Q: Mammator Mbaye ) Find the derivative of the expression - carefully. Do not simplify. (81) - 24r + 22…

A: To find out the derivative.

Q: ← A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet…

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Q: ical numbers r = -1 and x = 2 are found from a continuous derivative the second derivative is f"(x)…

A: Topic:- application of derivatives

Q: Let G(x) = sec 0 do for a in [0,]. Find G'(a).

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Q: The base of the solid is the triangle enclosed by x + y = 11, the x-axis, and the y-axis. The cross…

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Q: Evaluate d2y/dx2 at the point (0, -9). x = t3 - 3t y = 3t2 - 9

A: Given: x = t3 - 3t y = 3t2 - 9

Q: dr 4+x² S Choices: tan ¹(x + 2) + C 1 In x² + 4 +C In x + 2+ C 1 tan 2 1 ¹ 1/2 + +C

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Q: I. Find the solution set of the following. 2(1 + cos x) sin x 3. tan X 2 x = [0, π]

A: We can find the answer in the following steps.

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

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Q: Which of the following shows the expansion of 2-5n? n-0 O(-18) + (-13) + (−8) + (−3) + 0 O(-3) +…

A: To find the expansion of the given expression, substitute n=0,1,2,3,4 in the given expression.

Q: IV. Fill in the blank to make each statement true. Use correct notations. 3. If a polynomial…

A: We can solve this as follows:

Q: Estimates of  ∞ n = 1 1 n2  can be accelerated by writing its partial sums as  N n = 1 1 n2  =  N…

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Q: Given that answer = [*f(x) dx = 45 13 > [². what is f(v)dv?

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Q: 1/3 0 4x dx √25-x

A: Given Problem:- ∫0134x25-x4dx

Q: A function is given below. Determine the average rate of change of the function between t = 6 and t…

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Q: A ball bounces to a height of 6.1 feet on the first bounce. Each subsequent bounce reaches a height…

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Q: A sequence is shown in the graph. (1,6) 2 (2, 3) (3, 1.5) (4, 0.75)

A: Given Figure :-

Q: A construction worker is pouring concrete stairs. The first step requires 1.8 cubic feet of…

A: Concept: Arithmetic sequence: The series where the common difference between any two next words…

Q: at f'(2) = 6 and f'(6) = -2. Which of the following i there is a local minimum at x = 4 he function…

A: Topic:- calculus        Critical value:-  Where f'(x) = 0  And maximum minimum occurs called…

Q: Determine the appropriate rotation formulas to use so that the new equation does not contain any…

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Q: {an} is a geometric sequence. a5 = 2, ag = -54 find a 11

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Q: Find the volume of liquid needed to fill a sphere of radius R to height h = R.

A: answer is in next step. please give a like!!

Q: A particle is moving with acceleration a(t) = 30t + 10. its position at time t = 0 is s(0) = 7 and…

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Q: If [ 2013 |檳 sin ada = −a³ cos x + 3x² sin x + k fæ sin ædæ, find k d. 3/2 a. 6 b. -3/2 C. -6

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Q: 1 cos³x -dx =

A: The given integral is 1/Cos3x.

Q: What is the explicit equation for the nth term of the arithmetic sequence 6, 3.5, 1,-1.5, 4,...?…

A: We have: a1=6 -- the first term   Next, we calculate the common difference d=a2-a1 So, we have:…

Q: Which one of the following equations could work for the following graph? y = 5 y = -5…

A: To find,  the equations could work for the given graph.

Q: 1 4. fv³ (a²-v²) dv

A: Given problem:- ∫v3a2-v212dv

Q: IV. Fill in the blank to make each statement true. Use correct notations. 4. The graph of y = sin x…

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