Please help with # 14 thanks

Q: Use the Laws of Logarithms to combine the expression. In(a + b) + In(a - b)- 7 In(c)

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Q: Approximate the area under the graph of f(x) = 0.03x - 2.56x² +88 over the interval [4,12] by…

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Q: Use the values to evaluate (if possible) all six trigonometric functions. (If an answer is…

A: tanθ  is undefined        and        sinθ<0

Q: (f) [cos 2 x cos 2x e dx

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Q: The parametric equations and parameter interval for the motion of a particle in the xy-plane are…

A: x=6sint,y=5cost ,0≤t≤2π

Q: 4 '6 6x√x + 1 dx

A: Evaluate the definite integral. ∫466xx+1dx

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Q: 5. C r² = sin 20

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Q: (a) (b) 100 5 010 -5 0017 101 012 000 1 -2 8 0 syster O The system has a unique solution. (x, y, z)…

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Q: Two years ago, $9,000.00 was placed into an investment in which the amount of money present, P.…

A: Two years ago, $9,0000 was placed into an investment in which the amount  of money present, P, grows…

Q: The cost C'(x), where x is the number of miles driven, of renting a car for a day is $53 plus $0.65…

A: Given: The cost C(x), where x is the number of miles driven, of renting a car for a day is $53 plus…

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Q: Find div F and curl F if F(x, y, z) = xz7i+ 6y¹²x²j + 6z²yk. div F= curl F=

A: To find div F and curl F if Fx, y, z=xz7i+6y12x2j+6z2yk.

Q: Usain Bolt set a new world record for the 100 m dash in 2009 in Berlin. He ran 100 m in 9.58 s. a)…

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Q: Evaluate the triple iterated integral. /4 π/4 cos e [*¹* [*¹²ª [ * * p². 10 p² sin cos o dp de dé

A: The given integral is: ∫0π4∫0π4∫0cos θ ρ2sin φ cos φ dρ dθ dφ

Q: 5. Find the relative extrema and points of inflection for f(x) = 5xe*. Show all steps.

A: To find out the relative extrema and points of inflection for the given function.

Q: Suppose that 374 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

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Q: y = -45 + + x6 x7 Using calculus give a sketch of y. Make sure you include the following include the…

A: y = -45 + 2x6 + 120x7 Domain, The denominator cannot be 0. Therefore, x ≠ 0x ∈ (-∞, 0) ∪ (0, ∞)…

Q: A box (with no top) is to be constructed from a piece of cardboard of sides A and B by cutting out…

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: Here given function is f(x)=5-4x-3x2;[-5,4]

Q: Find all the antiderivatives of the following function. Check your work by taking the derivative.…

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Q: 7. Find real numbers a, b, and c so that the graph of the function y = ax²+bx+c contains the points…

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Q: A function f(x) and interval [a, b] are given. Check if the Mean Value Theorem can be applied to f…

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Q: (+ z≥ 0. unts) Set up the triple integral to calculate the volume of the region inside the sphere p…

A: Given,  Density = ρ = 8 z ≥ 0 Volume, V =? Let the spherical region is represented by 'D'. General…

Q: A rectangular storage container with an open top is to have a volume of 20 cubic meters. The length…

A: The volume of the rectangular storage container with an open top is 20 cubic meters. Let L be the…

Q: Given parametric equations and parameter interval for the motion of a particle in the xy-plane…

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Q: 12. Find the coordinates of the points on the curve y = 8 -- 16 x

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Q: Consider F and C below. F(x, y) = 1 + x² i + 2y arctan(x) j C: r(t) t² i + 7tj, = 0 ≤ t ≤ 1 (a) Find…

A: For solving given problem

Q: Express the limit as a definite integral on the given interval. lim n → ∞

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Q: A bacteria culture starts with 620 bacteria and grows at a rate proportional to its size. After 6…

A: A bacteria culture starts with 620 bacteria and grows at a rate proportional  to its size. After 6…

Q: Determine the intersection of the line defined by [x,y,z]=[2,-5,3] + t[3,0,5], t and the plane…

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Q: Find the area of the surface obtained by rotating the given curve about the x-axis. ㅠ x = 35…

A: we have given parametric curve x=35 cos3θ  and y=35 sin3θ

Q: Evaluate the line integral, where C is the given curve. √xy xy ds, C: x = t², y = 2t, 0≤t≤ 3

A: Short Explanation::-

Q: Use a graphing utility to graph the region bounded by the graphs of the functions. f(x) = -x² + 6x…

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Q: Let f(x) = 4x² + 2x - 8. Answer the following questions. 1. Find the average slope of the function f…

A: SOLUTION:-   Here given function,    f(x)=4x2+2x-8(a) We need to find the average slope of the given…

Q: 17. r = 4 cos 30

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Q: Five years ago, you acquired a 30-year loan of $130,850, charging 6.5% annual interest, compounded…

A: we have to need two formulas. They are:

Q: Consider the function f(x) = 2x³ - 6x² interval [-4, 9]. Find the average or mean slope of the…

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Q: D r=4+3 sin

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Q: Consider the function f(x)=√x near x = -1. Find the linear approximation error when using the linear…

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Q: Find the volume of the solid generated by revolving the region bounded by the given curve and lines…

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Q: Find the following using the table below. 1 22 X 3 f(x) f'(x) 4 2 g(x) 1 g'(x) 4 h'(3) if h(x) = =…

A: From given table  f3=4 , f'3=1 g3=3 , g'3=1 hx=fx·gx

Q: Find the average value of f(x,y)=xy over the region bounded by y=x² and y=56x.

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Q: Which polar coordinate pair labels the same point as the one shown below? 4x Select all that apply.…

A: We have to find the coordinates that label the same point.

Q: Let u = 4i + 5j, v = -4i +2j, and w = 3i - j. Determine the i, j form of each of the following: (a)…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: If an = F(n) and Eidn is Series of positive terms d Convergent ว Based only on the comparison test,…

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Q: Discrete Math  n = 2k for some integer k by definition of even. Write 4k2 + 5 in the form of even n…

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Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function (x) = 9x…

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Q: 2. Use logarithmic differentiation to find if y= dx 4x Show all steps.

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Q: The function f(x) = 2x³ − 42x² +240x + 7 has one local minimum and one local maximum. This function…

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