Combine the following into just one log function. (a) 3log(3x+1)+4log(x²-1) Answer: log( (b)log321 +2log33 Answer: log3 [√x+

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

A: x=4cos⁡(2t),y=4sin⁡(2t),0≤t≤π

Q: Find the Maclaurin series for f(x) = e-²x. Find the interval of convergence.

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Q: What is the lim f(x) for the following graph? X-0 5 4 V

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A: Given integral,Solid E is between the sphere of radius 1 centered at the origin on the top and the…

Q: Find the value or values of c that satisfy the equation the following function and interval. f(x) =…

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Q: Find the volume of the region bounded by the planes 4x + 2y + 3z = 5, y = x, x = 0, z = 0.

A: 4x+2y+3z=5,y=x,x=0,z=0.0≤z≤(5−4x−2y)3z=0⇒y=5−4x2x≤y≤5−4x25−4x2=x5−4x=2xx=56

Q: Given the following limit Select all that apply Olim f(x) exists. which of the following must be…

A:

Q: the U.S. postal service will accept a box for domestic shipping onl if the sum of its length and…

A: Let b be length of the box and a be the length of the side of the square.The volume V of the box…

Q: 8. Rewrite CLI x+2 dydadz in the order dzdxdy.

A: We need to change the order of integral.

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A: The objective of this question is to find the rate of change of the distance between Uniontown and…

Q: Obtain the following limits: lim (1+ x48 1 lim x-0 3x X 1 sin 3x

A: L=limx→∞(1+1x)x

Q: The demand function for a certain book is given by the function x = D(p) = 50e-0.004p. Find the…

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Q: blem #3: The inverse Laplace transform f(t) = -¹ {F(s)} of the function e-25(6s - 8) F(s) = S² +49…

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Q: Find the Taylor series for f(x) = ln(x) about a=2. Find the interval of convergence.

A: Taylor series of ln⁡(x) around a=2A Taylor series is given by f(x)=∑k=0∞f(k)(a)k!(x−a)k

Q: Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the…

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Q: (ii) Given f(x) = ¹ and the interval [1, 3]. Find the average value of f on the given interval. Find…

A: The given function is

Q: Calculate 7 af Әх af af af af 7 Әх ду Әх af ах af ду (1, -1) (1, -1) f(x, y) = x4y3 - х = = = , and…

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Q: Given the graph of f(x) below, find the graph of the derivative of f(x). 1-6-5-4-3-2-1 1.7

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Q: The area of the region is (Type an exact answer, using as needed.)

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Q: Please calculate whether this function is also differentiable, as well as continuous. Thanks.

A: Continuity at x=a:Differentiability at x=a:

Q: If the marginal revenue (in dollars per unit) for a month is given by MR = -0.3x + 400, what is the…

A: If the marginal revenue (in dollars per unit) for a month is given by To find the total revenue from…

Q: 1 1 Find the area of the surface generated by revolving the curve x = cos (4t), y = 2 + ¯sin (4t) on…

A: x=14cos⁡(4t),y=2+14sin⁡(4t) on 0≤t≤π4 about the x-axis. ddxsin⁡(ax)=acos⁡(ax)ddxcos⁡(ax)=−asin⁡(ax)

Q: Let F(x) = f f(t) d t Sa f(t) dt, where f is the function whose graph is shown. Evaluate F(7)

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Q: Find the following for the vectors v=6i +j and u = 9i + √3j. a. v u, vl. lul b. the cosine of the…

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Q: Sketch the graphs of the functions. f(x) = x³+x²- 2r and g(x) = 0 -4 y 2 2 - 2 Find the area of the…

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Q: Question 2 Drug sensitivity. One hour after x milligrams of a par- ticular drug are given to a…

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Q: Use complex number operations to determine the solution to the expression below. The final solution…

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Q: A person invests 4500 dollars in a bank. The bank pays 5.25% interest compounded monthly. To the…

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Q: Let f(x): = 10 - 2x. (a) Sketch the region R under the graph of f on the interval [0, 5]. y 10 8 6…

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Q: The function f(x) = x¹ = 7x³ +9x² +27x - 54 can be factored in the form f(x) = (x-r₁)(x - ₂)². Using…

A: From graph zeros are ● The graph crosses the x-axis at .  with multiplicity 1● The graph passes…

Q: What is A’(x) for this picture?

A: We need to find A'(x).

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Q: Problems 1-10, multiple choice. 1. What is the average value of y = e* on the interval [2, 7] ? A.…

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Q: 40 b) lim- 0-0 tan(20)

A: To find:-

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Q: (a) Eliminate the parameter to find a Cartesian equation of the curve.

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Q: 29. a(t) = -32; v(0) = 70; s(0) = 10 30. a(t) = -32; v(0) = 50; s(0) = 0 31. a(t) = -9.8; v(0)=20;…

A: 29) a(t)=-32, v(0)=70, s(0)=1031) a(t)=-9.8, v(0)=20, s(0)=0

Q: The total revenue from the sale of x stereos is given by R(x)= 3,000| 1- sale of x stereos, R(x). O…

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Q: 32. Assume that f is continuous and S f(t)dt = sinx -x cos.x. (a) Determine f(π). (b) Find f'(x).

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Q: Find the first 4 nonzero terms of the Maclaurin series for f(x) using the defi- nition of a…

A: Consider the function

Q: |ữ|= 3, |v|= 2, and the angle between # and (when placed tail-to-tail) is 45°. Find 27 +3v. 11 12…

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Q: Evaluate the spherical coordinate integral 2π π/3 3 S S S 4p² sin dp do de. & 0 seco

A: I=∫02π∫0π/3∫sec⁡ϕ34ρ2sin⁡ϕdρdϕdθUsing the Power Rule∫xndx=xn+1n+1+C

Q: Use Newton's method to find the positive fourth root of 5 by solving the equation x4-5=0. Start with…

A: .

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Q: Sketch the curve with the polar equation r = 2 + 2 cos(0). What is the name for the shape of the…

A: Given that the polar equation

Q: √3x + 16-5 x-3 18. lim- x 3

A: we need to find out the limit.

Q: Question The graph of f(x) is shown below. Find the graph of f'(x). 6-5-4 -2. 21 H 2 1 3 4 5 6

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Q: Consider the following relation. y = x + 2 Step 1 of 2: Find four points contained in the inverse.…

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Q: 2) Calculate: a) lim- √x-3-1 x²-16

A: We rationalize the numerator and use the formula (a+b)(a–b) = a2–b2.