Simplify the expression using only positive exponents: 24x7/2 25x 8x2/5 5

Q: (a) Identify the curve by transforming the given polar equation to rectangular equations. r=3cos0

A: according to bartleby guideline we do only first part of multiple r=3cosθin rectangle forn…

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Q: Use Newton's method to approximate a root of the equation 3x² + 6x² +4 = 0 as follows. Let x₁ = 3 be…

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Q: Find the limit of the sequence an = (−1)n-1n 3n² + 1 If the limit does not exist, type "Diverges" or…

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Q: Finding critical points and extreme values: The function f(x) = x(x² - 1) has two stationary points.…

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Q: Find the general solution to the homogeneous differential equation d² y dt² The solution has the…

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Q: Given f(x) = x² + 3x + 4, what is 07+h 2x+h+3 Oh+4 Oh² +7h f(2+h)-f(2) h equal to?

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Q: a. Use the Product Rule to find the derivative of the given function. b. Find the derivative by…

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Q: Suppose that f(x, y) = 2x + 4y at which −3 ≤ x ≤ 3, − 3 ≤ y ≤ 3. Absolute minimum of f(x, y) is…

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Q: function Finding critical points and extreme values: The f(x) = − x(x² − 1) has two stationary…

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Q: The position of an object in circular motion is modeled by the given parametric equations, where t…

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Q: ). Use the Integral Test to determine whether the sum converges. ∞ n = 1 1 n + 8 Evaluate the…

A: Given series  ∑n=1∞1n+8

Q: Given a nominal interest rate of 1.5% compounded daily (ie: compounded on each calendar day),…

A: Solution- Given Accumulated value after 9 years (A)=$20,000 Rate(r)=1.5% or 0.015 (annually)…

Q: Evaluate the limit using L'Hopital's rule 6 cos(7x)sec( – 3x) lim x →

A: limx→π26cos(-7x)sec(-3x)=limx→π26cos(-7x)cos(-3x)cosx=1secxit is 00 form use l'hospital rule

Q: Find the relative rate of change of the following functions and evaluate them at the given values.…

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Q: The marginal cost of the xth box of light bulbs is 10 + C(x) = [In(x + 1)] (x + 1)² 7 and the fixed…

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Q: y (x+5)(x + 1)

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Q: 66. 1 sin¹ x cos²x + cos² x sin² x -

A: The given trigonometric equation is 1-sin4x=cos2x+cos2xsin2x We have to verify the equation

Q: csc² x csc²x csc x cot x sin² x 1 + cos x 56. sec²x + tan²x = 1 + 2 tan² x 54.

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Q: Find the vertex, focus, and directrix of the parabola. 7x + 3y2 = 0 vertex (x, y) =

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Q: Suppose that we use the bisection algorithm to approximate r = √20 which the greatest zero of the…

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Q: The speed of a runner increased steadily during the first three seconds of a race. Her speed at…

A: Given: t (s) 0 0.5 1.0 1.5 2.0 2.5 3.0 v(ft/s) 0 5.7 9.2 15.5 18.8 19.4 20 To find the lower…

Q: Given f (x) = 3x + 2 – 1, what is f –1(x)?  f –1(x) = log3(x – 1) + 2  f –1(x) = log3(x + 1) – 2…

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Q: Analyze the following limits and find the vertical asymptotes of f(x) = a. lim f(x) x-12 b. lim f(x)…

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Q: For the function f(x, y) = 3x² — 5xy — 5y² + 4x − 3y + 5, find a unit tangent vector to the level…

A: The given curve is: f(x,y)=3x2-5xy-5y2+4x-3y+5

Q: 1. 3 (6-x²)²

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Q: a. Find an equation of the tangent line at x = a. b. Use a graphing utility to graph the curve and…

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Q: Suppose a Cobb-Douglas Production function is given by the following: P(L, K)= 70L0.9 K0.1 where L…

A: Given :- PL,k=70L0.9K0.1 L=units of laborK=units of capital

Q: Evaluate each limit. √2x² +2 x-2x+2 6) lim Find the equation of the line tangent to the function at…

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Q: You need to construct an open-top rectangular box with a square base that must hold a volume of…

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Q: 1. Find the equation of the tangent line to the graph of the function implicitly defined by the…

A: given that, 3y+cos(y)=x2  and ordinate is 0 find the equation of the tangent?

Q: A firm manufactures a commodity at two different factories, Factory X and Factory Y. The total cost…

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Q: Test the series below for convergence using the Root Test. n=1 4n + 1 3n+3 f(n) The limit of the…

A: Given query is to apply root test.

Q: What is the independent variable in the given differential equation? * d²y Ət ² O x Oy and t Ot O x…

A: To determine the independent variables in given differential equation

Q: 1) Consider the function f(x) = 5x+2. Use basic formulas from Geometry to calculate the Definite…

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Q: Which of the following functions (there may be more than one) are particular solutions to the…

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Q: Evaluate the integral by converting to polar coordinates. 3 6² 6² cos(x² + y²) dy dx = 0

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Q: 7. Find values of a and b that make the function below both continuous and differentiable at x =/…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Decide whether the series k=1 1 k7 + 3k + 6 converges.

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Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 600…

A: we need to find out the dimensions that will minimize the cost.

Q: (a) Find the arc length function for the curve y = In(sin(x)), 0 < x < , with starting point s(x)= =…

A: Given that y=lnsinx  ,0&lt;x&lt;π   starting point is π2,0To find :Arc lengthSolution :Arc length…

Q: Concept check: Evaluate the following integrals: ¹.ſ- dx (6-x²)z NIVE

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Q: The fox population in a certain region has an annual growth rate of 7 percent per year. It is…

A: NOTE: Refresh your page if you can't see any equations. . the exponential function is given by…

Q: Evaluate the sum k(4k+5). 9 9 Σk(4k+5) = k=1 (Simplify your answer.)

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Q: For the sequence, determine if the divergence test applies and either state that lim n→∞ an does not…

A: Given: an=limn→∞nn+2

Q: places. Find the direction in which the maximum rate of change occurs for the function f(x, y) the…

A: we will find the required

Q: Let z(x, y) = дz & მა Calculate дz მა дz Ət || || 7x2 - 9y2 where x дz St by first finding ?х дз' >…

A: The given function is  z(x, y)=-7x2-9y2 where x=-8s+5t and y=8s+3t

Q: Find the general solution to the homogeneous differential equation d² y dy dt² dt The solution can…

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Q: Evaluate n= 2 Then 10 n² - 1 First find the partial fraction decomposition of 10 10 n² 1 n² 1 n=2…

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Q: The demand function for a Christmas music CD is given by q= D(p) = 0.25 (225 - p²) where q (measured…

A: As per bartleby guidelines we only give first three questions answers. Please repost for other…