graph of the equation x2/3+2/3-82/3 is one of a family of curves called astroids because of their starlike appearance (as shown in the accompanying figure). Find the length of this particular astroid by finding the length of half the first-quadrant portion, y = (82/32/33/2 Esxs8, and multiplying by 8.

Q: -1 1 3 Evaluate the following limits. Write dne if the limit does not exist. lim f(x) = x-1 lim f(x)…

A: We have to find the limits.

Q: Given than [(x) f(x) dx = 7 and f (x) da = -5, which of the following is NOT TRUE 6 ® [f(x) dx =…

A: Given that ∫-23fx dx=7 and ∫36fx dx=-5, then to determine which of the following is not True.A…

Q: All continuous functions have antiderivatives. (A) True B) False

A:

Q: Using Simpson's method off, no spaces) Blank 1 0.66 √√x dx for n= 4 is equal to 0.66 (use 2 decimal…

A: As we know from the Simpson's Rule: ∫abfxdx=∆x3fx0+4x1+2fx2+4fx3+2fx4+...+4fxn-3+2fxn-1+4fxn-1+fxn…

Q: The marginal cost function in a company is given by C' = 70 - 0.7x where x is the number of units…

A: Please see the below picture for detailed solution.

Q: Find two polar coordinate representations for the rectangular coordinate point (-√2, √6), one with…

A:

Q: S dx (1+x) √x

A: Given,I=∫11+xxdxSubstitute  u=x(u2=x)Differentiate du=12xdx2du=1xdxThereforeI=∫21+u2du

Q: The average rate of change of f(x) = cos(x) with respect to x as a changes from 0 to π is 2 OOO 2 -2…

A: We have to find the average rate of change.

Q: 3- Find the length of the curves in Exercises 1-4. X = (y3/2/3) - y¹/2 from y = 1 to y = 9

A:

Q: 6 Consider the three by three system of linear equations 2x + Y + + 2y + 2z 5z 12. We will solve…

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Q: In 2000, an investment was opened with an initial deposit of $1800. The investment had grown to…

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Q: Evaluate indr 1-sin

A: To evaluate: ∫1+sin⁡x1−sin⁡xdx Let I =∫1+sin⁡x1−sin⁡xdx

Q: Atmospheric pressure P in pounds per square inch is represented by the formula P = 14.7e-0.21x,…

A: Given :Atmospheric pressure : P=14.7 e-0.21xx= number of miles above sea level

Q: dP The population of a town grows at a rate defined by the differential equation dt population in…

A:

Q: Find the length of the curves in Exercises 1-4. x = (y³/2/3) - y¹/2 from y = 1 to y = 9

A: Solution of given question is written in below steps.

Q: 3. The small circle is tangent internally at (-2, 0) to a big circle. See the figure below Find the…

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Q: 1. Solve the following equations: c) (x² - 4xy – 2y²) dx + (y² + 4xy – 2x²) dy = 0 -

A: Given :x2-4xy-2y2dx+y2-4xy-2x2dy=0

Q: 2xy - 3x²) dx + (x2² ty) dy = 0

A:

Q: Find the absolute maxima and minima of the function on the given domain. T(x,y) = x² + xy + y² - 9x…

A:

Q: in how many ways can we arrange the integers 1, 2, 3, 4, 5 in a line so that there are no occurence…

A: We use the principal of inclusion and exclusion.  For i∈1,2,3,4, let Ai ⊂Si be the set of all…

Q: Find the average rate of change of the function over the given interval. f(t) = 13+ sint a. 0, 플] п…

A: As we know that; The average rate of change between the interval t1≤t≤t2 is given by: Average rate…

Q: Consider the R 2 − R function defined by f(x, y) = 3x + 2y. Prove from first principles that lim…

A: Let's evaluate given R2-R functions limit.

Q: y dx y = 9x+8 Find dx

A: The given function is: y=9x+8   As we know that; The Sum/Difference Rule: f±g'=f'±g' The Power Rule:…

Q: Find the absolute maxima and minima of the function on the given domain. T(x,y) = x² + xy + y² - 9x…

A: Given :T(x,y)=x2+xy+y2-9x+3

Q: The length of a rectangle is given by 4t - 3 and its height is 2t, where t is time in seconds and…

A:

Q: Find the area of the region bounded by the curves below. Sketch its graph and shade the region. 1.…

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Q: Solve the following system of inequalities 2x+y-8>0 3x-y+6>0

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Q: 11. x² +1 Find +3x+1 -dx

A:

Q: Find the determinant by row reduction to echelon form. 1 3-2-4 01-25 -1 1 2-8 6 4 -2 -3 3

A: 1. Row echelon form

Q: Find an equation of the line tangent to the graph of f(x) = a) at (1,1); b) a (-37) at a) The…

A:

Q: Acceleration due to gravity in feet per squared second is the constant function a(t) = -32. Suppose…

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Q: The quotient of z1 =6 cis (2/3); z2 =2 cis (1/6) in trigonometric form is;

A:

Q: 2) Find the average value of the function f(x, y) = 6x + 4y over the plane region R. defined by the…

A:

Q: In Problems 1-4, find the Laplace transform of the given function. Determine a condition on s that…

A: Given :f(t)=sin3tf(t)=etcost

Q: The proper way to evaluate f(x + h) for the function f(x) = 3x²-x+4 is f(x + h) = 3(x+h)² - x +h+4…

A: Topic:- function

Q: Consider the following matrices: [2 3 id -1 27 - - A = B = 3 0 C = 1 0 b 4 1 Perform the following…

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Q: 2 Let f(x) = 5x4 -/+8√x-3. a) Find f'(x). (b) Find an equation for the tangent line to the graph of…

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Q: What are the vertices of the hyperbola whose equation is: * 9x² -4y² +72x + 108 = 0 (-1,0) and…

A:

Q: Find the area bounded by the parabolas y2 = 4x and x2 = 4y

A: Given curve: y2 = 4x and x2 = 4y To find the area between y2 = 4x and x2 = 4y First find the…

Q: A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day. Write an…

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Q: Ут. У 4+ 2 ly мв a.

A: The given series,       ∑k=1∞2k4+k

Q: Find fxy.

A:

Q: Forces of 19lbs and 40lbs act on a body producing a resulting force of 50lbs. What is the angle…

A: The given two forces are 19lbs and 40 lbs. The resulting force is 50 lbs. Because the resultant is…

Q: use differentials to approximate 1. 64 .05 2. e^0.99 3. square root of 101 6 the value

A: Solution is here

Q: Let y = f(x). Which of the following statement is TRUE? O None of the above O Let f(x) = -2x + 4. If…

A:

Q: We start from the expression for the contact force 4 a³ 1/21 F=E (₁ 7² - (07*³²¹) ³²) '8γπa3 E* 3 R…

A: We have to find the differentiation of the above equation.

Q: 8) Maximize the function f(x, y) = 16-r² - y² subject to the constraint x + y = 6

A:

Q: .. Consider the quadratic function y = 4-x². Using the limit definition, ind the derivative of the…

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Q: 2.f(x) = = x3 3. f(x) = x tan x 4.f(x) = +₁₁ 4* x-1 1 x7

A:

Q: When an object is dropped, the distance it falls in t seconds, assuming that air resistance is…

A: Given