Of all rectangles with a perimeter of 18, which one has the maximum area? (Give the dimensions.)  The rectangle has the maximum length ___ and width ___.

Q: Find the local maximum of f(x,y) = xy(1-x-y) Find the critical point(s) and check the value of D = f…

A: given function

Q: Use partial fractions to find the power series of the function: 52+74 (x − 9) (x + 8)

A: f(x)=5x+74(x−9)(x+8)5x+74(x−9)(x+8)=Ax−9+Bx+8

Q: Question 4.11) Compute the following limits at infinity. A) lim D) lim Chapter 4: LIMITS (SECOND…

A: As per our guidelines, you are supposed to answer only one question with a maximum of three sub…

Q: tan (x) = sin(x)

A:

Q: Tutorial Exercise Consider the given function. f(x)=4- Evaluate the Riemann sum for 2 S x S 14, with…

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Q: Solve the following integration :- 3 S sin³x Sin³x cośx dx

A: The given integration is

Q: 1. Use Elementary Row Reduction and Gauss elimination to solve the following linear systems: { (a).…

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Q: Find the Maclaurin series for the given function. 3e-x

A: A Maclaurin series is given by f(x)=∑k=0∞f(k)(a)k!xk

Q: Determine whether I 5Mm Converges or diverges. If 6 7m m=2 Converges, find its sum

A: Geometric Series∑n=1∞a⋅rn−1 Converges if and only if −1<r<1∑n=1∞a⋅rn−1=a1−r

Q: Use the Ratio Test to determine whether onvergent conditionally, or divergent. n=1 (−77)” n! is…

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Q: 10. Consider the following two 3 x 3 matrices -1 3 3 1 -2 -1 1 -2 -2 (b) ( (c) A = 1 1 AB and BA. (…

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Q: Use the transformation u = 3x + 4y, v=x+4y to evaluate the given integral for the region R bounded…

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Q: Find the general Solution of: 2² dy dx = x² x e

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Q: A note card company has found that the marginal cost per card of producing x note cards is given by…

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Q: for f(x) Verify that the hypotheses of the Mean-Value Theorem are satisfied √49 – x² on the interval…

A: we have given that

Q: pлd¹ The rate of flow, Q of a fluid through a pipe of diameter, d and a length, L'is given by Q…

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Q: Gonzalez Manufacturing borrowed $39000. Part of the money was borrowed at 8%, part at 10%, and part…

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Q: Assuming that a 380-foot tall giant redwood grows vertically, if I walk a certain distance from the…

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Q: Find all functions f(x) such that 7x f'(x) - and f (0)

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Q: Find the arclength of the curve x = -t³. 123 1²³, y = 2/1/1² t² with 2 ≤ t ≤7.

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Q: A pilot is flying over a straight highway. He determines the angles of depression to two mileposts,…

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Q: Determine the Fourier transform of the following signal: x (t) = è¯(t-1) u(t-1)

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Q: (a) Find the number a such that the line x = a bisects the area under the curve below. 1≤ x ≤4 a =…

A: The region under the curve,  To find the value of b such that the line bisects the area

Q: The graph of the derivative f'(x) is given below. On what interval(s) is the function f(x) concave…

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Q: Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x)…

A: The Taylor series:Where centered at .

Q: Write an integral in the form A region. Answers must be exact. As a suggestion, graph the equations…

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Q: Express the limit as a definite integral on the given interval. 72 Part 1 of 2 lim Σviln(2 + x) Δ.,…

A: The definite integral  can be written in a limited form on the interval [a,b] as

Q: Consider a system of 3 equations with 3 unknowns. If the augmented matrix has been correctly reduced…

A: Here we have to general results for finding the solution

Q: Find all relative extrema. Use the Second-Derivative Test where applicable. (If an answer does not…

A: To find all relative exrema of the following function.

Q: Evaluate the indefinite integral as an infinite series. | arctan(x3) dx ]) + c C ( n = 0

A: The given integral .The aim is to solve the indefinite integral as an infinite series.

Q: With your computer now loaded, you bring up the data for · your experiment. The data suggests that…

A: Given: To Find: To Find the inverse relationship so that the amount of time it will take to reach a…

Q: A. f(x): = Match the common function with its Maclaurin series. 1 1 x B. f(x) = (1+x)" C. f(x) = cos…

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Q: a) The rectangles in the graph below illustrate a ? The value of this Riemann sum is 0 and this…

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Q: Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a. f(x) = 2 In (x), a = 1

A: A Taylor series is given by f(x)=∑k=0∞f(k)(a)k!(x−a)k

Q: fum of a cide wing Voled vp TH A dx TRIGONOMBTC SUTION Ja-yX-4 dx-aast de Ja². (asing)" (acest do)…

A: We need to dirve the formula of area of circle

Q: tan x dx

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Q: * Find dy dx = the general Solution of :- - X+3x2 √x² + 2x³² 2

A: We use the variable separable method to solve the given differential equation.

Q: Find the equation of the tangent to the curve cos²x - sin²x y = at the point where x = I |4

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Q: Determine whether the graph is that of a function. If it is, use the graph to find its domain and…

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Q: f(x) = x2 + 2ax+ 2 si 4 si ba +1 si x≤-1 -1 <z <3 z≥ 3

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Q: Find the future value P of the amount Po= $200,000 invested for time period t = 9 years at interest…

A: To find the future value P of the amount invested for time period years at interest rate…

Q: The marginal cost for printing a paperback book at a small publishing company is C'(p) = $0.013 per…

A: Production Cost function is given by where c(p) = marginal cost function

Q: Verify that the two planes are parallel. -x + 6y + 3z = 6 1 x + 2y + z = 7 3 Find the normal vector,…

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

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Q: Solve the following triangles: (a) a = = 10, b = 8, c = 7 (b) A = 90°, B = 20°, a = 7;

A: To solve the triangle, we use the Law of Cosines to find one angle of the triangle and the Law of…

Q: 1. With a programmable calculator (or a computer), it is possible to evaluate the expressions for…

A: Given that the region under the curve  from The right endpoint sum

Q: f(x) = = x²-7x-8 x-4 For each entry, enter a single number. First Number: The smallest x-intercept…

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Q: Find f such that f'(x) = f(x) = √x¹ f(1) = 13. ***

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Q: Use a graph of f (x) = 2 sin (x²) to determine where an antiderivative, F, of this function reaches…

A: Given that F is antiderivative funtion of function

Q: A rectangle has its base on the x−axis and its upper vertices on the parabola y = 9−x^2. Find the…

A: Given that a rectangle has its base on the x−axis and its upper vertices on the parabola To…