2. Find the derivative of the function & write your answer in simplified, fully factored form. y = (x² - 4x)³(2x³ + 3x²²

Q: What is an antiderivative of the function x + 2xln(x)? x²ln(x)+2023 xln(x) +2023 In(x) + x xsin(x) +…

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Q: A lake initially contains 5000 fish. Suppose that in the absence of predators or other causes of…

A: A lake initially contains 5000 fish. Suppose that in the absence of predators or other causes of…

Q: Solve the formula for k 7k + ka a = f

A: Use multiplication rules

Q: A normal vector to a line is perpendicular to that line. True O False

A: To find true or false statement: A normalvector to a line is perpendicular to that line

Q: O Make a graphical tool to approximate the limit of the function. If necessary, round to three…

A: The limit of a function can be found by using the graph or by finding the table of values to the…

Q: The first line does it read d/dx(x^h)=h*x^h-1 ????

A: The given rule ddxxh=hxh-1. We have to explain the formula.

Q: Find two unit vectors orthogonal to both (2, 8, 1) and (-1, 1, 0). (smaller i-value) (larger…

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Q: Let f (x, y) = e(5x-6y). Find the equation for the tangent plane to the graph of f at the point (1,…

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Q: Compute the partial sums S2, S4, and S6 of 1 1 1 1 + + + 3.5 5.7 7.9 9.11 (Use symbolic notation and…

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Q: SLO A. Evaluate definite and indefinite integrals graphically, numerically, and analytically, using…

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Q: (b) Find a power model and a quadratic model for the data. (Round all numerical values to four…

A: We have given a table that shows the national expenditures for health care in the United States for…

Q: Ja 3 x√x - 2dx

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Q: Write a polar equation for a conic having focus at the origin, directrix x = e = 5. r = Enter theta…

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Q: Multiply and simplify completely: √12x³y¹5. √√6x²y-7 Your answer will be in the form A√B, where A…

A: We need to multiply and simplify the given expression.

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A: ∫xndx=xn+1n+1+C ∫1xdx=lnx+C

Q: lim x →∞ lim x →∞ 77-3x+71 cx77-71 ax ax77-3x+71 cx74-71 ax74-3x+71 lim x →∞ cx77-71 = AY AY

A: we need to find the given limits

Q: In three-space there are four possibilities for the intersection of two lines. True False

A: We have to find whether the given statement is true or false. In three-space there are four…

Q: The function H(t) = −16t2 + 48t + 12 shows the height H(t), in feet, of a cannon ball after t…

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Q: Problem #3: Consider the following matrix. A = d a b C f (a) Suppose that det(A) = −6. Let B be…

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

Q: Given the polar equation r = The eccentricity is e = 5 The equation of the directrix is: 7 6 sin(0)'…

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Q: The owner of a skating rink rents the rink for parties at $360 if 30 or fewer skaters attend. For…

A: Solving the problem

Q: Represent the sum of the complex numbers −3+2i and −3−i on the complex plane. Use the Point and…

A: Given that -3+2i and -3-i To determine the sum

Q: ƒ ( 1 ) = 1 ² 0 1²) find f' (2) (2 decimal places) Using the Product r

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Q: 2. The normal line slope of f(x) = (a - 1)x² + 3x - 2 is GIN at x=-2, a=?

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: (ln(t))4 dt t

A:

Q: 3. Find the linear unbounded operator A and its domain D(A), and write the system in the form U₁ =…

A: We need to find the linear unbounded operator A and its domain D(A), and write the system in the…

Q: Determine the following limit: 2e 2x Him (2²-2-2) x-0

A: limx→02ex-2x-25x2

Q: Consider the following vector function. r(t) = (3t2, sin(t) - t cos(t), cos(t) + t sin(t)), t> 0

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Q: 25 lim x+c+ (x-c)³ 25 lim x+c¯(x-c)³

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Q: S sinxdx 7+ cos²x

A: integration ∫sinx7+cos2xdx

Q: 9. A = (2, a 3) and B = (-1,-2) are - perpendicular each other, a=?

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Q: Find the area enclosed by the ellipse a² b + y=-b√√√a²-x² y² 62 b y=1/√√a²-x² = 1 shown in the…

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Q: Estimate S M₁~ e -x2 dx using the Midpoint Rule with n = = 4, correct to 5 decimal places.

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Q: Given that v = (0, -2) and w = (5, -8), what is w - v? A (5,6) B (5,-6) C (-5, -6) D (-5, 6)

A: Explanation of the answer is as follows

Q: Calculate the Taylor polynomials T₂(x) and T3 (x) centered at x = a for f(x) = 20.sin(x), a =…

A: Here we have given a function: fx=20sinx, a=π2 So, here we need to calculate the Taylor Polynomial…

Q: For the function, evaluate the given expression. y) = \n(x² + y²), find g(0, e) g(x, y) g(0, e): =

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Q: Use Lagrange multipliers to maximize the function f(x, y) subject to the constraint. (The maximum…

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Q: The following table gives the millions of metric tons of carbon dioxide emissions in a certain…

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Q: Part a) Use the steps demonstrated in this module to find an equation for the logarithmic function…

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Q: A particle that moves along a straight line has velocity v(t) = t²e-8tm/s after t seconds. This…

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Q: What is the polar form of the equation? (x+6)² + y² = 36 O² 12r cos 0 Or(r+ 12 cos 0) = 0 ○r (r + 12…

A: x+62 + y2 = 36

Q: Find sin(8) O√3 -|~ 2 √2 2 이틀 2 TT 5T/6 7m/6 2/3 4/3 TT/2 3T/2 ○ TT/3 5/3 _TT/6 /11/6 0

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Q: 4. Find the distance between the planes: 4x+3y-2z=20 and 4x+3y-2z=-11. a. Find any point P on the…

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Q: What is the area between the curves y= integrating with respect to x.). O ! (6) WIN = ² and y=-x² +…

A: y=x2 and y=-x2+2x

Q: What present value amounts to $358,312.09 if it is invested for 5 years at 16% compounded…

A: What present value amounts to $358,312.09 if it is invested for 5 years at 16% compounded…

Q: s dx ²√x² x² - 81 x² x = 9 sec (0)

A: ∫dxx2x2-81

Q: 38. f(x) ex 1 + ex

A:

Q: Using the coffee demand function, Q = 8.56-p-0.4ps +0.1Y, show that sugar is a complement for…

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Q: What is the component form of resultant of 46 - 5ā? a = (1, -3) 6=(-1,2) Enter your answer by…

A: a=<1,-3>, b=<-1,2> Find 4b-5a

Q: What is the approximate volume of the solid created when the region under the curve y = sint on the…

A: The solid created when the region under the curve :  y = sin(x) on the interval [0,π] is rotated…