Let h(t) 4t6 + 6t Determine the most general antiderivative of h. (4t6 + 6t¹)dt C

Q: Find the surface area of the part of the plane z = 2x - y − 3 that lies inside the - cylinder x² +…

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Q: Given the graph of f(x) below, find the graph of the derivative of f(x). Select the correct answer…

A: From the given graph

Q: Let f be the function defined as f(x) = { 1 3x-4 for x <3 for x ≥3 Which of the following statements…

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Q: Consider the following function on the given domain. P(x) = (x + 1) + 3.x ≥ −1 Step 2 of 2: Find the…

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Q: 2) Find the first derivative given that f(x)= 5x √2x+3

A: we need to find out the first derivative of the given function."As per the rules, we are supposed to…

Q: Determine the relative extrema for the function: y=2xe^x Group of answer choices relative minimum…

A: The objective of this question is to find the relative extrema of the function y=2xe^x. Relative…

Q: Suppose k(x) = f(g(h(x))). Given the table of values below, determine k'(-2). f(x) g(x) h(x) f'(x)…

A: xf(x)g(x)h(x)f′(x)g′(x)h′(x)−2−4−1046−7062−11−3820−5−8237

Q: 15. 3 + sin y=y-x³

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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: 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: Which of the formulas below could be a polynomial with all of the following properties: its only…

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Q: f(x) -10-9 6 4 2 -1 9 5 2 1 O -1 -3 0 12 m s 9 7 00 10

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Q: When calculing the inverse Laplace transform of the function F(s)=6/s^5 is obtained as a result: A-…

A: To find the inverse Laplace transform of the following function.

Q: (j) Evaluate the following line integrals, where C is given (i) fcds where C: x = t³, y = t¹,1 ≤t≤4

A: Consider the line integral

Q: Find two numbers whose sum is 9 and whose product is a maximum. The two numbers are (Simplify your…

A: The objective of this question is to find two numbers whose sum is 9 and whose product is a maximum.…

Q: Find af ах af ду af дz Әх af af af af and I Әх ду дz Find their values at (0, -1, 1) if possible.…

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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: Sketch the described region of integration. 0sys1, sin ysxs 2 Choose the correct sketch of the…

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Q: For the following trajectory, find the speed associated with the trajectory and then find the length…

A: We need to find speed and length of trajectory.

Q: Provide your answer below: p'(x) =

A: Given that the expression

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) /co: COS(π/X5) +6 dx

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Q: The marginal revenue of the xth box of flash cards sold is  200e−0.003x dollars per box.  Find the…

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Q: Find an equation for the hyperbola described. Graph the equation. Center at (-6,-8); focus at…

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Q: 1. Write the binomial expansion of the expression: (2x² − y)³

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Q: Question 1 Suppose the Sunglasses Hut Company has a profit function given by P(q) = -0.03q² +3q -…

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Q: Determine if the following function is continuous and differentiable at x = 0. ex - sinx 13x² + cos…

A: We need to determine if the function is continuous and differentiable.

Q: For the function  below, determine the open intervals where it is decreasing. f(x)=(x+4)^2/3 Group…

A: The objective of this question is to find the intervals where the function f(x) = (x+4)^2/3 is…

Q: Find the radius of convergence, R, of the series. Σ(-1)^ (x-4) 6n + 1 n = 0 R = 00 Find the…

A: The given series is (-1)n(x-4)n/(6n+1), n from 0 to infinity.

Q: an open box is made by taking an 8cm by 10cm sheet of cardboard and cuttign square corners whose…

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Q: Find the binomial series for the function (1 +4x)ª. The binomial series is

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Q: A solid E is bounded by the sphere z = -x² - y² on the top and the xy-plane (z = 0). The projection…

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Q: Determine if the following function has an inverse function. Answer r(x) = (x+4)³ Or has an inverse…

A: We know that, a function y = r(x) has an inverse function if it is one-to-one i.e. if for each…

Q: 2 lim 9x² (e-3/x²-1) = X→∞ (Simplify your answer.)

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Q: ketch the graphs of the functions f and g. 1 f(x) = g(x) = 2x − 1 O O -10 10 6 4 2 L2 -1086-2 -6 -8…

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Q: We have 36 ft2 of material to build a box of maximum volume with a square base and no top. What is…

A: Let side of base square = x ftLet height of box = h ftThe figure of box

Q: 2. Consider the curve y = sinx - on the inteval 0 ≤ x ≤ π/2. (a) Sketch the curve and shade in the…

A: (2)The curve is given as, on

Q: Find af ax af ду af az af af af "7 ах ду ду = af 11 -(0, -1, 1) = and Find their values at (0, -1,…

A: The Power Rule:The Chain Rule:

Q: The wind-chill index (in degrees C) is modeled by the function W = 13.12 + 0.62157- 11.370.16 +…

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Q: A company estimates that the revenue (in dollars) from the sale of x doghouses is given by the…

A: The objective of this question is to find the approximate change in revenue when the sales of…

Q: Your weekly cost (in dollars) to manufacture x bicycles and y tricycles is C(x, y) = 24,000+ 64x +…

A: Weekly cost to manufacture x bicycles and y tricycles is

Q: Calculate af ax af af ax af Əy (1, -1) af af af af ax' ay ax (1, -1) ay (1,-1) f(x, y) = 7,000 - 65x…

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Q: Let f(x) = -20 +7x² - 3x Determine the critical values of f. If multiple such values exist, enter…

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Q: 2. Find the Maclaurin series of the following functions. 1. f (x) = xm 1-x³9 2. f (x) = x² sin² (4x)…

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Q: ) Rectangular bathtub has a fixed height of 10ft. The length of the bathtub is increasing at a rate…

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Q: Find two positive numbers such that the sum of one and the square of the other is 300 and whose…

A: Given that two positive numbers such that the sum of one and the square of the other is 300 and…

Q: Question sin What is y'(x) when y(x) = (4x³ + 6x)* ^? Enter an exact answer in terms of a natural…

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Q: f(x) = 3x5 f'(x) = 2 이집

A: Given that the function

Q: Determine q'(x) when q(x) = 8(4¹) X4 Sorry, that's incorrect. Try again? q'(x) = |

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Q: Of the following, which are solutions to the differential equation y" - 5y +6y=0 ? 1.y = e²t II. y =…

A: The differential equation is given byThe auxiliary equation corresponds to the differential equation…

Q: model for the surface area of a human body is given by the function S = f(w, h) = 0.1091w0.425,0.725…

A: We have given a function that gives surface area in terms of weight and height. We have to calculate…