Find the indefinite integral. Hint: u = x-5 implies x = u + 5. [x(x-5)³dx

Q: Consider the following parametric curve. x = sin(t), y = cos²(t); (√2, 1) Find an equation of the…

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Q: Find the Taylor For n = 2, P₂(x) = For n = 4, P₁(x) = polynomials of degree n approximating cos(2x)…

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Q: Consider the series n=1 an where an = √n +5(n+3)! en-7 In this problem you must attempt to use the…

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Q: Suppose that the monthly marginal cost for firefighting portable water tanks is C'(x) fixed cost of…

A: To solve the following problem

Q: and and simplify the expression and yd Booze (Cos+isin)³ ress the answer in standard form, a + bi.

A: Given query is to find the a+ib form.

Q: Which of the following is the appropriate substitution for the Bernoulli differential equation xy -…

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Q: -45 + 7(x + 2) - 6x (no justification needed) = -45+ (7x + 14) - 6x = -45+ (14 + 7x) - 6x = (-45 +…

A: Part 2 Given that , -45+7x+2-6x For each step, use a property of the real numbers.

Q: Using identities to simplify completely trigonometric expression below :  tan x (csc x - sin x)…

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Q: A clothing company determines that its marginal cost, in dollars per dress, is given by the funtion…

A: NOTE: Refresh your page if you can't see any equations. . the marginal cost function is  where…

Q: If sin x=3/5, x in quadrant I, then find (without finding x) : sin(2x)=___ cos(2x)=___…

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Q: 11 = 2 A 1 as the sum of a vectory in W and a vector z in W+. 2 and 1₂ = a -13]. b , find a, b, and…

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Q: 25-year old woman burns 200−20t cal/hr while walking on her treadmill. Her caloric intake from…

A: Given query is to find the calories decrease in 4 hours.

Q: Simplifying the logarithmic expression log, b³ - 3 log, a + 5log, a¹b will give you m+nlog, a The…

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Q: Show that the given curve c(t) is a flow line of the given velocity vector field F(x, y, z). c(t) =…

A: We have to show the following conditions according to the given information

Q: Question Find the area of the region enclosed by r = 5 cos (0). Enter an exact answer. Provide your…

A: Please see the below picture for detailed solution.

Q: A -| n=3 n 3"

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Q: et = 8 M8 n=0 en n!

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Q: Determine if lim x →3 √x+6-3 x - 3

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Q: The point x O is a regular singular point of the given differential equation. Find the equation for…

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Q: Suppose that the monthly marginal cost for smokejumper harness straps is C'(x) = 3.5x +95 and the…

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Q: f(u) -Using the u-substitution, u = x + 3, identify f such that the integral√x +3 dx, takes the form…

A: ∫xx+3dx

Q: The population of a town is now 40,000 and t years from now ill be growing at a rate of 300 sqrt of…

A: Let Pt be population of town at any time t

Q: Determine the value of 3f(x)g(x) lim x-2 3f(x) - 2g(x)

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Q: Find the point on the graph of f(x)=√x that is closest to the point (9, 0). -([ (x, y) =

A: The objective of the question is determine the closest point to the given point and graph.

Q: Use the Ratio Test to determine if the series converges. 80 7(k!)² Σ 4(2k)! k=1 Select the correct…

A: NOTE: Refresh your page if you can't see any equations. . the given sequence is  substitute k+1…

Q: Use the Divergence Test to determine whether the following series diverges or state that the test is…

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Q: ← Find the future value P of the amount Po invested for time period t at interest rate k, compounded…

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Q: Find the following antiderivative. J dx (x ln x) In (In a

A: To evaluate the antiderivative

Q: Coefficients Linear in two variables. Find a general solution of the differential equation (y - 4x -…

A: We know  ∫xdx/(x²+1)= (ln|x²+1|)/2  ∫dx/(x²+1)= tan-1(x) or arctan(x) Given differential equation,…

Q: 1. Bernoulli's Equation. Find a particular solution of the differential equation y^2dx + (2xy -…

A: solution is below.

Q: Find the area under the curve y = 4x³ over the interval [0, 2]

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Q: Determine the relative extrema of f, if there are any, and locate any saddle points. a. f (x, y) =…

A: To solve the following problem and find the points of extrema

Q: Use an appropriate test to determine whether the series converges. Σ k=1 k! 7kk

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Q: Suppose that a particle moves along a straight line with a velocity v(t) = 4 - 2t, where t is in the…

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

Q: Find the indicated partial derivative: Y Ə dy y + 2x = [

A: Given query is to find the partial derivative.

Q: Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not…

A: Here, we need to simplify 18 sin4x. So,              18 sin4x=18sin2x2               =181-cos(2x)22…

Q: 2. y6y" + 8y' = 2x² cos3x

A: Solution: Given data, y"'-6y"+8y

Q: Find 3xe Select one: O a. O b. da. Hint: use substitution. (e-1) (1-√e) (1-e¹) ○ c. O d. (1-e)

A: ∫xndx=xn+1n+1+clet x2=t2xdx=dtwhen x=0, t=0when x=1,t=1

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

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Q: What would projvu be?

A: We have to find the projvu.     According to our guidelines we can solve only one question so please…

Q: 2x - 7 lim X→2+ x - 2

A: To find the given one sided limit

Q: Consider the following parametric curve. Find dy dy dx dy x = sin(4t) + cos(t), y cos(4t) sin(t) 4…

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Q: Find the area of the finite region bounded be curve y = -x² + 4x - 3 and the x-axis, fr x = 2.…

A: Given query is to find the area under the curve.

Q: The graph on the next page shows the velocity v(t) of a runner in metres as a function of time t in…

A: Aim: We need to underestimate and overestimate the distance covered by the runner in first 5…

Q: 1) Find the general antiderivative of the function y = O 0.1Ln/x^3+x) + C O 10Ln|x^3+x| + C…

A: Given query is to find the integral.

Q: . Let f(x) = ka. Determine the constant a so that f(-1) = 10 and f(2) = 5 19 4

A: Given query is to find the constants of the function.

Q: If the marginal revenue for ski gloves is R'(x) function. R(x) = = - 0.6x + 50 and R(0) = 0, find…

A: If the marginal revenue fro ski gloves is R'x=-0.6x+50 and R0=0, to find the revenue function.

Q: Question Convert the equation r = 6 cos(0) + 3 sin() into an equation in rectangular coordinates.…

A: in polar coordinates   x=rcosθ   and  y=rsinθr2=x2+y2given  r=6cosθ+3sinθ

Q: Let a = -3 [33] 9 105 41 and 6 = b Compute the projection of a onto b and the vector component of a…

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Q: A tank originally contains 100 gallons of fresh water. Then water containing 0.25 lbs of salt per…

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