evaluate the following integrals:

Q: Here are three functions that are related to each other. Correcti Tries: 3 One is f(x). Another is…

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Q: Find the average rate of change of the function from X1 to X2 Function x-Values f(x) = x2 - 4x + 6 X…

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Q: A particle travels along a straight line with velocity function v(t) = e'sin(2t) + cos(t) – 1 cm per…

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Q: Given the functfion f(x) = ax³ sin(x) + be" , where a and b are nonžero, real numbers. 1. Find f'…

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Q: VV1+x/xdx 5.

A: Integral

Q: 12

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Q: 2 xy' + 3y = 3 –

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Q: Answer the question. Show ALL your steps in your calculations. Answer in complete sentences. 8…

A: ----------------------------------------

Q: aluate the indefinite integral. (Use C for the constant of integration.) (x+11)V 22x + x² dx Need…

A: Given query is to find the integral.

Q: 1. Which of the following is 'alse? * If x > 0, then 1/x > 0. O If x > 1, then x*2 > x. O If x<y,…

A: Please see the answer below.

Q: III. Find the area of the regions bounded by the curves. Draw a figure showing the region. 8. y =x;…

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Q: 2. Find the integral 2x+3 dx x2-9 a. In/(x – 3)³(x + 3) + C а. b. In[(x – 3)³(x + 3)] +C c. 2ln[(x –…

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Q: Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements…

A: Given problem:- Two sides and an angle (SSA) of a triangle are given. Determine whether the given…

Q: 1 dr r²Vr² – 9 -2.

A: answer is in next step

Q: 5. f(x) = x(12.x + 8) 7. f(x) = 7x²/5+ 8x-4/5 %3D

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Q: Find all the local maxima, minima, and saddle points ne function. f(x,y) = /56x2 - 8y² - 16x – 31…

A: When a function has the largest value it is called local maxima  and when it has the smallest value…

Q: Let f(x) = (8x2 + 6x + 11)/(7 - 7x²). The horizontal asymptote is given by y = ? Round your answer…

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Q: Three vectors are given by: J = 2î – k K = 2î – ĵ+ 2k L= 2î – 3} Determine: (i) K•L x J; and (ii)…

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Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

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Q: The cost, in dollars, of producing x yards of a certain fabric is given by C(x) = 84 + 0.16x –…

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Q: 1. lim 32-3 +5 2. lim log, (x-8x 1) 3. lim (In 2x +5) + 4 Write your final answer using 4 decimals

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Q: 1. Determine the type and stability of the critical points of the homogeneous systems: dx (a) = x –…

A: we have to check stability of critical points

Q: 3. You are designing a spherical tank to hold water for a small village.The volume of liquid it can…

A: Given information: V = Volume of tank m3V = πh23R-h3…

Q: The expression p sin ø cos 0 in spherical coordinates is equivalent to what expression in Cartesian…

A: given expression ρsinφcosθ

Q: Give the substitution that converts the given nonlinear equation into a linear equation then find…

A: We need to find solution of differential equation.

Q: What is the probability you draw two cards of the same color from a standard 52 card deck you are…

A: favourable conidtion is  26C1*25C1 = 26*25 total condition is 52C151 C1 = 52*51 probability =…

Q: The position s of a point (in meters) is given as a function of time t (in seconds). 1 ;t = 1 S =…

A: The position s of a point in meters,   s=73t2-1t; t=1

Q: 12)List the first five berms of Ehe regence a,=6, aan= 5a -4 as=3 a=? asz?

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Q: An iron block weighs 5.2 N and has a volume of 272 cm³. What is the density of the block in kilogra…

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Q: dV = vt+1+t where V 4. The volume of a balloon is increasing according to the formula dt cm³ is the…

A: To solve the given differential equation and find an expression  for V(t).

Q: Consider a triangle where A = 30°, a = 1.5 cm, and b = 1.6 cm. %3D 16 ´B A (Note that the triangle…

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Q: 27. f"(1) = 12 + sin 1 28. f"(t) 29. f'(x) = 1 + 3x, f(4) = 25 30. f'(x) = 5x- 3x? + 4, f(-1) = 2…

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Q: 53-58 A particle is moving with the given data. Find the posi- tion of the particle. 53. v(t) =sin t…

A: We know that if 's' is position of a particle at a particular time 't' then velocity v (t) and…

Q: the mapping notation for this function 2. Given the function F(x) -4 *+2 al Determine the mappina…

A: we have  f(x)=4123x+3-2 the domain of the given function is (-∞,∞)and range of the given function is…

Q: A farmer is constructing three equally-sized pens against the side of a barn for his animals, as…

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Q: Find the time required for an investment of $2500 to grow to $5500 at an interest rate of 5.4% per…

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Q: 8. 21

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Q: 5 ,2 X |x² + x – 6| dx -5

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Q: 2. Determine the derivative of g(t) = 8°[(2t + 1)² + t].

A: Given that     g(t) = 8t[(2t+1)2+t]

Q: Calculate the derivative by expanding or simplifying the function. 1- 2(19t) s(t) (19t)l/2 (Use…

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Q: Region is bounded by y=x y=x2 Rotate about x=2. Find the area. Please help

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Q: Problem 1 Solve the following basic calculus problems: d (e* cosx dx а. b. Jy**dy d? c. Show: dx d…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Problem 3. Sketch the region enclosed by the curves y = 6x, y=4x², and find the area of that region.…

A: We can solve as follows

Q: The given matrix is an absorbing stochastic matrix in standard form. Idently R and S and compute the…

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Q: Šolve the optimization problem. Maximize P xyz with x + z = 9 and y + z = 9, and x, y, and z > 0.…

A: Note thate there are three variables and our goal is to express two of those as a function of…

Q: The integral Sr Si rdz dr do represents the volume of a solid. What is the solid? half a cylinder…

A: Cylindrical coordinates :       x = r cosθ , y = r sin(θ) , z=z where,    x2+y2 = r2   and θ =…

Q: Evaluate the line integral Vo dr for the following function o and oriented curve C (a) using a…

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Q: 5x and S(x): = 20 + 2x. Round only Find the consumer's and producer's surplus if for a product D(x)…

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Q: Rewrite the series to show that it is an alternating series of the form E1(-1)"b„. Then, use the…

A: The given series,          ∑n=1∞n cosnπ2n

Q: Answer the question. Show ALL your steps in your calculations. Answer in complete sentences. 2x²–50…

A: fx = 2x2-50x2+8x+15domain: -∞,-3∪-3,∞x=-3, vertical asymptotex=-5, hole