Use the Second Derivative Test to find all relative extrema. h(t) = -x + 6x² - 4

Q: Test for convergence / divergence. Find the limit if result is convergence.

A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines

Q: Evaluate the integral. SSS_* √x² + z² av E where E is the region of integration bounded by the…

A: To solve this put x=rcos(theta) And z=rsin(theta)

Q: The curve has an equation of r = 4sin0. Compute the area bounded b the curve. 12.57 11.18 16.89 O

A: Given :r=4sinθ

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Q: 1. Evaluate L²S³ (2y³ + x²y) dx dy

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Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

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Q: (b) lim *+1 √√2x+6-2 x²-1

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Q: Find I must find the indefinite integral then I need to use the result to calculate the definite…

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Q: For which values of n is the function ya solution of the differential equation xy"-Kxy'-6y=0

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Q: an = an-1/n

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Q: (c) 0$ y = cos (√√x² +1) (d) y 2x 2x +1

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Q: Evaluate the improper integral or state that it diverges. P -dx Select the correct choice below and…

A: The given integral is: I=∫2∞32x2dx   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 And…

Q: Given Cost and Revenue functions C(q) =q³-9q² +53q + 5000 and R(q) = -3q² + 2500q, what is the…

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Q: Derive implicitly—Implicit differentiation. Please show a detailed solution. Also, comprehensive and…

A: In this question, we want to differentiate the given expression implicitly.

Q: Sketch the graph of y = x-2 (x+3)²

A: The horizontal asymptotes by comparing the degrees of the numerator and denominator. Vertical…

Q: 5. Find the area bounded by the parabola y = x^2 - 3 and the line y =1.

A: Given problem:- Find the area bounded by the parabola y = x2 - 3 and the line y = 1 .

Q: IV. Directions: Find the derivative of the following functions. x²+³√x+√x+28 22-26. f(x) = VX 27-31.…

A: We have to find derivative

Q: The concentration of a drug in a patient's bloodstream is given by the function C'(t) = 0.15t…

A: Explained below

Q: Match each of the following vectors with its magnitude. t=(-7, 1) a. 5√2 u = -21-8j b. 2√√5 a vector…

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Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A: Given :Hight of a ball in t isf(t)=-16t2+374t+15

Q: Given m = 6, n = 1, and v = (-4, 7), what is v(n-m)?

A: Given :- Given m = 6, n = 1, and v = <-4, 7>, what is v(n-m)?

Q: The price of a popular gaming console is related to the quantity demanded by the equation 2p² + x² =…

A: We need to differentiate the equation and calculate the unknown.

Q: 1. Use Comparison Test to determine the converges or diverges of the series Σ: 8 n=1 (n+1)√n

A: By using Comparison Test to determine the convergence or divergence of the series ∑n=1∞ 1n+1n.

Q: II. Directions: Find the slope of the line tangent to the given curve at the indicated point 10-12.…

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Q: Consider the general solution of a differential equation is y=C₁x-C₂ ln x² find C₁ and C₂ when…

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Q: Given that Inx+3 f(x) = 3lnx-1 Find the formula for f−¹(x). State the domain of f−¹(x). Show all…

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Q: 21,n *** a1,1 1,2 1,3 02.n ... 0 02,2 02.3 0 0 03,3 03.1 ... 1 0 00 Onn, field K and n € Z₂1.…

A: The matrix,M:=a11a12a13..a1n0a22a23..a2n00a33..a3n............00000ann∈Matn×nK be an upper…

Q: ƒ sin (3x³) dx

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Q: Problem 7. Find the limit lim f(x), where 2--2 x²-4 2+21 x-2

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Q: A farmer wants to fence an area of 6 million Square feet in a rectangular field and a divided in…

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Q: The solution of the differential equation y' + 2xy = Ky when y(1)= K is

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Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2 and y = 2x…

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Q: Graph a vector, opposite to the given vector, that has an initial point at the origin.

A: In order to graph the opposite vector we need have one more point along with the origin.

Q: Convert the degree measure to radian measure. Round to three decimal places. −46.23°

A: Convert the degree measure to radian measure. Round to three decimal places. −46.23°   Please show…

Q: 12. Find the equation of the tangent line to the polar curve r = 2-sin(0) at 0 = 1/3. Draw.

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: A company produces a special new type of TV. The company has fixed costs of $496,000, and it costs…

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Q: Evaluate the following limit, if possible. If the limit c 4 lim 42-√√

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Q: Solve the linear ODE using an Integrating Factor. dy dx - 3y = 8e5x

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Q: The current population of a small town is 2104 people. It is believed that town's population is…

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Q: 1. -3 Given that 9+x² following functions: (−1)n+1 Σn=0 32n+1 1. f(x) = 5 arctan x2n. Obtain the…

A: We have to obtain power series representation.

Q: Partial Sums An arithmetic sequence has a first term of -1 and a common difference of -17. If S₁,…

A: We have to find the sum

Q: III. In each of the following, express the required series in summation notation. TL 2. Find the…

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Q: For the function defined as follows, find all values of x and y such that both fx(x,y) = 0 and fy…

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Q: (d) Use the given information to write an Lauation that relates the variables x and y.

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Q: An 84 cm wire is cut into three pieces. The second piece is 4 cm longer than the first piece and the…

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: sinhr²-² 2 1. lim r+0 sinhr−r

A: To evaluate: limx→0 sinh⁡x2−x2sinh⁡x−x Given limit is of 00 form L'Hospital's rule tells us that if…

Q: Help

A: Please refer to the image below

Q: -.f x³ ex² dx 3

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