he area formed in the first quadrant by the graphs of y = x² and y = 8 - x²

Q: Sketch the parabola, and label the focus, vertex, and directrix.. (a) (y-1)=-12(x+4) (x−1)² = 2(y-2)…

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Q: lim (2x-1)(3-x) (x-1)(x+3) is

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Q: Let A = -4 2 [33] - 3 - 4 Find - 2A. - 2A =

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Q: 11 [ f(x) dx = 8 and f(a)da 94 at g(x)dx= 10 and [ 94 h(x) dx = 23,

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Q: Perform the indicated operation if possible. -6 6 9 1 28 I -7 5 80 17 ... Select the correct choice…

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Q: Estimate the area under the graph of f(x)=x2 +x+1 over the interval [3,8] using ten approximating…

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Q: 4. Find the total distance traveled by a particle that has velocity V(t) = 2t -4 over [0,5]

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Q: Find cos (2² +3³)dA where D = {(z, y) | 25 ≤ z² + y² ≤ 64} . Round your answer to four decimal…

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Q: Find the local maxima and minima for the function f(x) = x² + 3x - 4. If there is more than one…

A: this is the question of calculus  here function is given  we have to find the maxima and minima of a…

Q: Consider the following acceleration a = a=32, v(0) = 10, s(0)=6 , initial velocity, and initial…

A: formula used  a=dvdt∫xndx=xn+1n+1+c

Q: Suppose f(x) is defined as shown below. a. Use the continuity checklist to show that f is not…

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Q: Determine if the following series is convergent or divergent. Show all work, give thorough…

A: We have to determine given series convergent or divergent

Q: A ball is thrown from a height of 72 feet. Its position above the ground is given by the formula…

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Q: Fill in the missing values below one at a time to find the quotient when x³ - x²-16x-20 is divided…

A: Given :x3-x2-16x-20 is divided by x+2

Q: Find Sn for the given arithmetic series. a₁ = 18, d = -3, n = 14

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Q: Show that the homogeneous 2 2 family of integral curves x² + y² v=vx. equation y' - = 2xy leads to…

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Q: the terminal point p(x,y) determined by a real number t is tiven. find sin (t), cos(t), and tan(t).…

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Q: (a) Interval = [-10, 0]. 1. Absolute maximum= 2. Absolute minimum = (b) Interval = [-7,2]. 1.…

A: We need to find out the absolute maximum and absolute minimum for the function given in the given…

Q: If [ f(a)da = f(a)da + f(a)da -f(x)da, what are the bounds of integration for the first integral? a=…

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Q: 1.f x²√3x + 2dx

A: The given integral is x2 sqrt(3x+2).

Q: K a. Use the definition mtan = lim x→a a. Mtan f(x)-f(a) x-a b. Determine an equation of the tangent…

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Q: Find the derivative. f'(x) = f(x) = x³ - 12x² + 36x - 4 Find any critical numbers of the function.…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: Find the domain of the function. (Enter your answer using interval notation.) g(x) = log4(x2 - 1)

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Q: 2-Solve S x-2 x²-4x+5 dx

A: The given integral is: I=∫x-2x2-4x+5dx   Use the common integral formula. ∫1ax+bdx=1alnax+b+C

Q: 7. f tanxdx

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Q: Find f(x) such that f'(x) = e7x - 6x and f(0) = 10.

A: f'(x)=e7x-6xf(0)=10f(x)=∫(e7x-6x)dx∫xndx=xn+1n+1+c

Q: Given y = 4z and y = 2² +3, describe the region for Type I and Type II.

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Q: If a rock is dropped from a height of 295 ft, its poistion t seconds after it is dropped until it…

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Q: 2. f(cosxsecxcotx)dx

A: To evaluate the integral by using substitution method

Q: Consider the following function. f(x) = x³ - 12x² + 36x - 4 Find the derivative. f'(x) = 3x²-24x +36…

A: Topic = Functions

Q: Let f and g be functions that satisfy the following properties: lim f(x) = 0 2+00 lim g(x) = 0 *+00…

A: Given :limx→∞1+fx5gxlimx→∞ fx=0limx→∞gx=0limx→∞f'x=4limx→∞g'x=2

Q: Find the quotient of polynomial expression using long method and synthetic division. 1. (x³ − 14x +…

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Q: Write the number 2.317 = 2.3171717... as a ratio of integers.

A: Given number :- 2.317=2.3171717.....

Q: Evaluate the following integral: 2x²-1 (3x-1) (x²+1) dx S

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Q: Evaluate the integral. Check your result by differentiation. (Remember the constant of integration.)…

A: We need to evaluate the integral: ∫x-1x2-2x+45dx

Q: Determine if the following series is absolutely convergent, conditionally convergent, or divergent.…

A: Given the series is  ∑n=1∞ -1n+1n3+1.

Q: The line tangent to the graph of g(x)=³-4x+1 at the point (2, 1) is given by the formula These…

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Q: Let f(x) be the function whose graph is shown below. 1 9

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Q: Find the velocity and acceleration vectors in terms of u, and up. r= a(4+ sin t) and 0=3-et, where a…

A: Given; r=a(4+sint), theta=3-e-t.

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

A: According to question,Given Function,fx = 3x2 -5x + 4x2

Q: 12. A rope is attached to the bottom of a hot-air balloon that is floating above a flat field. If…

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Q: 3. Consider the implicit relation 4x2y - 3y = x³. dy A. Use the technique of implicit…

A: according to bartleby guideline we do only first three part of multiple  4x2y-3y=x3d dx(xn)=nxn-1d…

Q: Find the volume of the region under the surface z corners (0, 0, 0), (8, 0, 0) and (8, 8, 0). Round…

A: Volume of the region is given by ∬f(x,y)dA

Q: Find the volume of the solid bounded by the paraboloids z = - 7+² + y² and z = 4- - y².

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Q: [x - yarctan()]dx + xarctan()dy = 0

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Q: Evaluate the following integral over the Region R. (Answer accurate to 2 decimal places). 11,³ R =…

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Q: 3. An arctic cold front is moving through an area. It is 37° when the temperature begins to drop.…

A: Let's find linear equation(temperature vs time).

Q: A cylindral drill with radius 2 cm is used to bore a hole through the center of a sphere with radius…

A: Volume of ring =Volume of sphere-Volume of cylinder

Q: A particle moves along the x-axis with acceleration given by a(t) = 27 sin (t) for time t≥ 0. If the…

A: Given Acceleration,at = 2π sin π2tat time t = 23,    velocity v = -6

Q: Find ²** (3z + 2y) ºdzdy

A: