My topic is about Higher Order Derivatives and Optimization for reference. A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 10 in by 17 in by cutting equal squares from the four corners and turning up the sides. Find the length of the side of the cut-off square so that the box has the largest possible volume.

Q: 2. Consider the function g(t) = (t+1) ln(t) on the interval [1, 3]. (a) Evaluate efg(t) dt. (b)…

A: Consider the function gt=t+1 lnt on the interval 1, 3. (a) To evaluate ∫13gt dt. (b) By using  part…

Q: Assume that functions f and g are differentiable with f(-3)=3, f'(-3)=2, g(-3)=2, and g'(-3)=2. Find…

A: Fx=fxgx We use product rule ddxuv=udvdx+vdudx

Q: Let us model the number of automobile sales in a developing country as 151,000 N (t) = where N is…

A: (a) To find the number of cars sold in 2010, we substitute t= 2010 into the equation:…

Q: 8) Find the Taylor expansion of f(x) at the given f(x)=√x, c=4

A: Given that , fx=x , c=4 find the Taylor expansion of fx at the given c.

Q: The owner of a ranch has 2,900 yards of fencing material with which to enclose a rectangular piece…

A: The owner has 2900 yards of fencing material, to enclose a rectangular piece of grazing land along a…

Q: A produce and distributor of gift cards produces a boxes of cards per day at an average cost C (x)…

A:

Q: 1. Consider the function f(x, y, z) = x²e³²² (a) Find the gradient of f at the point (1, 3,0). (b)…

A: Here we have given a function: f(x,y,z)=x2eyz2. To find the gradient of the function…

Q: 5) 2 [4x 4x + =dx X

A:

Q: A spherical dust particle, with a radius a = 0.101 mm and density of 1320 kg/m³, is sedimenting in…

A: Given a spherical dust particle, with a radius a = 0.101 mm and density of 1320 kg/m³, is…

Q: Describe a viewing rectangle, or window, that shows a complete graph of the polar equation and…

A: We have to graph the given function. This equation is in polar coordinates so first we will put…

Q: Find an equation of the plane. The plane through the point (8, 9, 3) and with normal vector 5i + j -…

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Q: f(x) =tan(ecot (x²))

A: We know that the derivative of tanx=sec^2x

Q: 13-R] [CLO 3] Simplify the expression a2 b5 c4 / a3(b2)-3d-4 so that each variable appears at most…

A: a2b5c4a3(b2)-3d-4=b5c4a3-2(b2)-3d-4=b5c4a(b2)-3d-4

Q: Construct the differential equation for the given exponential model. y(x) dy dx = 92e⁰.74x

A:

Q: Question #10 - Which integral best describes the area below? f(x)=x²-2x g(x) = x va 34 4 -1 7 2 7 2…

A: Area of the shaded region : Let y= f(x) and y=g(x) be two curve and f(x)≥g(x) on a,b , then the area…

Q: Find the derivative(s) of the explicit solution(s). dy (Use a comma to separate answers as needed.)…

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Q: 2. Describe a series of transformations that would transform f(x) = |x| +5 into g(x)=2x-1 Be sure to…

A: Describe a series of transformations that would transform f(x)= |x| +5 into g(x)= -2|x| -1 .

Q: Construct the exponential model that satisfies the given initial value problem. dy dx an 0.4y, y(0)…

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Q: Find an equation of the plane. The plane through the points (2, -1, 3), (7, 4, 6), and (-2, -2,-2)

A: Points ( 2 ,-1 ,3) , ( 7 , 4 , 6 ) and ( -2 , -2 , -2 )

Q: A particle travels on a curve given parametrically by (cos(2t), sin(3t)) where t is in seconds.…

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Q: Find the equation of a line tangent to the curve ²+²=9 at the point (2, √5). In addition, find the…

A: To find out the equation of the tangent line to the given curve at the point and also need to find…

Q: =y³ + x² + 4xy - 2x - 13y +7. For each of the points provided, determine 2. Consider the function…

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Q: A street light is mounted at the top of a 15-foot-tall pole. A man 6 feet tall walks away from the…

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Q: For the cost and price functions below, find a) the number, q, of units that produces maximum…

A: Cq=80+11qp=71-2q

Q: Find a parametric representation for the surface. the part of the sphere x² + y² + z² = 36 that lies…

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Q: Rotate area between y =6-X and y= x^2-6x about X-axis. Compute the volume (Washer Method)

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Q: The graph off shown below has vertical asymptotes at x = -5 and x = 6. Find the following limits.…

A: The graph of f shown below has vertical asymptotes at x=-5 and  x=6. To find the following limits.…

Q: Given the demand function D(p) = √250 - 4p, Find the Elasticity of Demand at a price of $13 At this…

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Q: A firm determines that units of its product can be sold daily at p dollars per unit, where…

A: As per the rules we are supposed to answer the first three subparts and rest others can be reposted.

Q: 12. f2cos² (4x)sin (4x) dx Туре. U= U' =

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Q: Classify each singular point (real or complex) of the given equation as regular or irregular. 3x²y"…

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Q: Use the suggested substitution to write the expression as a trigonometric expression. Simplify your…

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Q: Determine the equation of the hyperbola satisfying the given conditions. Write the answer in the…

A: Asymptote y=±xFoci=0,±7  Let the equation of the hyperbola is y2a2-x2b2=1

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to a or y.…

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Q: 1 Find the probability that a randomly selected value of X lies in the interval [4, 6] if f(x) = 63…

A: Probability density function : f(x) = x263 To find: the probability that a randomly selected value…

Q: Use the table to evaluate the given compositions. b.g (f (2)) e.f(f(f(1))) h.g(f(h (−1))) ah (g (3)…

A: As per Bartleby answering guidelines if a questions has multiple sub parts then an expert is…

Q: Find parametric equations for the line. (Use the parameter t.) The line through the points (0, ½, 1)…

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Q: Find the general indefinite integral. (Use C for the constant of integration.) fo Find the general…

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Q: (4) Find the following integrals. ³+1 (a) [de dt tvt (b) (2 sin (20) - 3eº) do (c)(√u + 1) du.

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Q: Consider the function f(x) = 5x + 3x¯ For this function there are four important intervals: (-∞, A],…

A: Given function is f(x)=5x+3x-1 Now first we shall find critical points then find whether the…

Q: Evaluate the following integral in spherical coordinates. 2 2 SSS ( x² + y² +2²) 19/2 dV; D is the…

A: So for cartesian coordinate to spherical coordinate the conversion formula isx=r sinϕcosφ,…

Q: Find the derivative ( of the following functions dx a.y = (4x² - 1)(7x³ + x) b.y = e²x cos x sin x…

A: As per Bartleby answering guidelines if multiple sub part question are posted in single pic then the…

Q: 1. For all n > 2,¹ 1, e, 4. For all n > e, arctan(n) n³ In(n) n In(n) >, and the series n >, and…

A: we are not allow to solve more than 3 subpart in each question.  Thank you

Q: 1. The biologist is studying the increase in population of a particular bacteria. The number of…

A: We have to find the number of bacteria in 2 hours and time when increasing rate is 48000/min.

Q: Given the equation 4r²-2y²=9, show that dy 1

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Q: Question 7: Find the general solution to the following, and show all work: y=[²₁1]y

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Q: The piece-wise function, f(x), is given below. Find values of a and b that would make f(x)…

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Q: 7. Find the derivative of the following functions: a. y = esinx b. y = (5x6x8)14

A: (a) given y=esinx

Q: Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the…

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Q: 2 2. Consider the series Σx-₁(-). Find a formula for the nth partial sum S, and k k+2 determine if…

A: we have given series ∑k=1∞ 2k-2k+2