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Q: Find the derivative of the function. y = ³√x²-x² 一 y' =

A: The given function is; y= x7/8

Q: 15. A hot-air balloon is rising straight up at 5 ft/sec. An observation area is located 80 feet from…

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Q: A= B n ed Use the right triangle and the given information to solve the triangle. a=1, c= 8; find b,…

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Q: 2 0 0 1 -2 1 0 4 -3

A: given matrix is ,

Q: Find the absolute maximum and the absolute minimum for the function x² x + 1 f(x)= x = Absolute…

A: The given function is; f(x)=x2/(x+1) , [-2.5,-1.9]

Q: (11,20) (11,20) Show that (40) fdx+ gdy = f(4,1) 24x²y³dx + 40y^³dy is independent of path: J(4,10)…

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Q: Find all points (x,y) on the graph of f(x) = 2x²-3x with tangent lines parallel to the line y = 5x…

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Q: If the marginal revenue for ski gloves is R'(x) = -0.5x + 55 and R(0) = 0, find the revenue…

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Q: Suppose limx→cf(x) = 5 and limx→cg(x) = -2. Find: a. limx→cf(x)g(x) b. limx→c2f (x) g(x) c. limx→c…

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Q: Consider the following position function. a. Find the velocity and speed of the object. b. Find the…

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Q: Find the average rate of change of the function over the given intervals. f(x) = 12x³ +12; a) [5,7],…

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Q: A thermometer reading 8°C is brought into a room with a constant temperature of 28°C. If the…

A: A thermometer reading 8C is brought into a room with a constant temperature of 28C. If the…

Q: Choose the correct graph below OA O OB. Oc W NE

A: The derivative of the downward parabola is the line with a negative slope.The derivative of the…

Q: Find the demand function for the marginal revenue function. Recall that if no items are sold, the…

A: R'(x)= 0.03x2-0.08x+189

Q: Find the indefinite integral and check the results by differentiation S(4x²+ + 3)²dx

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Q: 5. Solve y"" - 6y" + 11y' - 6y = 0

A: The given differential equation is

Q: 2. Σ. 1 (-5) 2n n2gn

A: The given series is The Root test If L<1 then series is absolutely convergent If L>1 then…

Q: Find the limit of the sequence an = (cos.n) 5"

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Q: Sketch the graph of the quadratic function. f(x) = x² — 20x – 800 - -

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Q: Suppose that we're making and selling some widget and the cost (in dollars) when making a widgets is…

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Q: 7. Determine critical points for each of the following functions. 2 d. y = x² 32√x e. y = x³ + 3x² -…

A: To determine the critical points for each of the following functions.

Q: Find the radius of conv- 00 n! n 1.3.5..... (2n

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Q: Derive the formula of a circle using horizontal strip

A: We need to derive the formula of the area of a circle by using horizontal strip

Q: Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and…

A: from the given table

Q: For the following exercises, use the Mean Value Theorem and find all points 0 < c < 2 such that ƒ(2)…

A: The given function is,Take derivative.Substitute x=c

Q: An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is…

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Q: Suppose parametric equations for the line segment between (4, 2) and (4, - 2) have the form: [ x(t)…

A: The line segment between the points (4, 2) and (4, -2) has parametric equations,It is also given…

Q: = 16 a Problem #3: Find the surface area of the part of the paraboloid z = 64 - x² - y² that is…

A: z=64-x2-y2x2+y2=16The surface area is given by

Q: Suppose you are given a triangle with Then a = , and b= 9. Enter your answers with at least 3 digits…

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Q: lim x-0+ x lim x-0-x² g. h. 2 1+x i. lim (¹+2) ² →? x-2

A: Note:-Since you asked multiple sub parts questions, according to our policy we can solve only first…

Q: at the point (0, 1/2). and b = The equation of this tangent line can be written in the form y = mx +…

A: y=1/[3sinx+2cosx]Point (0,1/2)

Q: (−1)" (x + 15)" Σ 10" 14 n=|

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Q: Use the method of substitution to evaluate each of the following general antiderivatives. 6x² (b)…

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Q: 9. Let f(x) = sinx, g(x) = cos x. The functions f and g, considered on the interval 0, π], are…

A: Given that the function are

Q: Find the indicated term of the binomial expansion. (√2₁² +1³); second term 3 u

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Q: Find the indefinite integral of the function g(x)=e^(2x) sin(3x)dx

A: The objective of this question is to find the indefinite integral of the function g(x) = e^(2x)…

Q: (a) Estimate the area under the graph of f(x) = 1/x from x = 1 to x = 2 using four approximating…

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Q: Use the formula f'(x) = lim Z-X f(x)=x²-x+4 f'(x) = f(z)-f(x) Z-X to find the derivative of the…

A: we need to find f'(x)

Q: A balloon is rising at a rate of 3 meters per second from a point on the ground 41 meters from an…

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Q: 1 e e 5. If A-), then ¹-(3) = eª = 01 0 e

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Q: Find the volume of the region under the surface z=xy^2 and above the area bounded by x=y^2 and x+y=2

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Q: Find the interval I and radius of convergence R for the given power series. (Enter your answer for…

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Q: Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate…

A: We have to find the number of calculators produced from the beginning of the third week to the end…

Q: Find the exact value of each of the following under the given conditions. 6√85 85 5 sin a = 13 (a)…

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Q: 61. Presale Order A wireless store owner takes presale orders for a new smartphone and tablet. He…

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Q: 5. Use Part one of the fundamental theorem of calculus to find the derivative of the following…

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

Q: 17. What are the dimensions of the right circular cylinder of greatest volume that can be inscribed…

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Q: 4. Solve Cauchy problem: y" - 5y' + 4y = 0, y(0) = 1, y'(0) = 2

A: To solve the following Cauchy problem.

Q: Evaluate the integral: 0 x = (A) Which trig substitution is correct for this integral? Ox= 16 sin(0)…

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Q: Consider the functions f(x) = 6 arcsin (6x) g(r)= 12arctan (a) Find the derivatives of f(x) and…

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