Find a positive number a such that the sum of 36x and is as small as possible. Does this problem require optimization over an open interval or a closed interval? A. open B. closed

Q: Generate the graph of f(x) = x + 2x + 3 with a graphing utility, and use the graph to find a number…

A: Here to find δ, we can use the epsilon delta definition of continuity which states that: f(x) is…

Q: Find two positive real numbers such that they add to 40 and their product is as large as possible.

A: Our Aim is to find two positive real numbers a and b such that they add to 40 and their product is…

Q: (2) The floor function is defined as a| = max{m e Z|m < x}. Effectively, the floor function is the…

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Q: ketch represents f(x) = x² + x – 6 and g(x) = -x - 3 M If MN = 3, calculate the possible length(s)…

A: Graph for a function is representation of function with respect to independent variable on axes.…

Q: Find k such that f(x) = x° - kx? + kx + 35 has the factor x - 5.

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Q: Find a positive number x such that the sum of 4x and is as small as possible. Does this problem…

A: Solution is given below:

Q: Find a polynomial of a degree n that has only the given zero(s). x=-8,5,3; n=3

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Q: If f'(x) and g'(x) exist and f'(x) > g(x) for all real a, then the graph of y = f(x) and the graph…

A: In this question we have to find how many time functions will intersect to each other.

Q: Find two positive integers whase. and Q2 is. with. product Sum. the the of one the Sovucre of other…

A: Disclaimer: Since you have posted multiple question, we will be posting  We will be using the fact…

Q: Find the largest number d such that if |x – 3| < 8, then |5x – 15| < ɛ, where ɛ = 1 Repeat and…

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Q: Given the interval (a,b), on the x-axis with the point c inside, find the greatest value for 8 >0…

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Q: A person in a boat 4 km from the nearest point P on a straight shoreline wants to go to point A on…

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Q: If h is defined by h(x) = lxl + 2 a) what is the range of h if the domain of h is yhe interval…

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Q: The base of a three-dimensional figure is bound by the semi-circle y = √4x². Vertical cross sections…

A: In the figure, the strip shows the width of the rectangle perpendicular to x-axis.

Q: Given two nonnegative numbers a and b such that a + b = 4, what is the difference between the…

A: Given ,          a+b=4             b=4-aGiven expression=a2b288   fa=a24-a288…

Q: B- Obtain PDE by eliminating the arbitrary functions from the following; 2- Ix + my + nz = Ø (x2 +…

A: We have to obtain PDE by eliminating the arbitrary function from  lx+my+nz = ϕx2+y2+z2.

Q: Find three positive integers x, y, and z that satisfy the given conditions. The product is 27, and…

A: for finding value of x,y,z we will property arithmetic mean is greater than equal to geometric mean…

Q: Find a positive number a such that the sum of 25x and is as small as possible. Does this problem…

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Q: DO Puanlar) 1 Which of the following is the domain of g(x)= sgn ? (Here ||a|| denotes the greatest…

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Q: Find two positive numbers whose product is 193 and whose sum is a minimum. A 0,193 1,193 193 2/193,…

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Q: Find the least integer n such that f (x) is O(x") for following function. f(x) = 17x +10x³

A: Given function is fx=17x4+10x3 We have to find the least integer n such that fx is Oxn. Since, the…

Q: Find the absolute max and min of the function f(x) = cubed root of x − x on the interval [−8, 1]

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Q: Show that for f(n) = n³ - (ri'log, n) + 2n E O(n³ ) A give the constants: (c, n) B:arguing that your…

A: When a function is bounded above by another function with a factor asymptotically, it is referred to…

Q: 8. ) Find the smallest values of x and y such that 27

A: Given query is to find the smallest value of x and y.

Q: 1. Find two non-negative numbers such that the product of the first squared and the second is 108…

A: 1) Given data:   The given expression for the product of the squared of the first number and the…

Q: Find the least value of “n" so that , k=n 1 199 Sn 2k-1 k=1 200

A: Given:          Sn=∑k=1n12k−1&gt;199200

Q: b) Find the largest possible domain A, where all elements of A are non-negative and f: A → R, f(x) =…

A: Solution:-

Q: Indicate the least integer n such that f(x) = (3æ³ + 2x²)(5æ5 + 4æ*) € O(x").

A: Finding f(x) explicitly using multiplication of polynomial. The highest power of x or degree of f…

Q: Find k such that F(x)=x^3-kx^2+kx+44 has the factor x-4

A: To find k such that F(x)=x3-kx2+kx+44 has the factor x-4.

Q: The figure above shows the design of a square quilt that consists of 7 nonoverlapping isosceles…

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Q: Find a positive number a such that the sum of 16x and is as small as possible. x = Does this problem…

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Q: Find three positive integers x, y, and z that satisfy the given conditions. The product is 8, and…

A: Use Lagrange method to solve

Q: Given an interval [a,b] that satisfies hypothesis of Rolle’s theorem for the functionf(x)=x4+x2−2.It…

A: Rolle's theorem states that "If a function f(x) is continuous on the closed interval [a, b] and…

Q: Given an interval [a,b] that satisfies hypothesis of Rolle’s theorem for the…

A: Given function is x3-2x2+3 .

Q: Find three positive integers x, y, and z that satisfy the given conditions. The product is 8, and…

A: Here, We have 3 positive integers x,y,z. Conditions are, x * y * z = 8…

Q: 4. Find the remainder of f (x) = (1 + x)3/² of degree 3.

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Q: Find all values of æ for which rank(A) = 2.

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Q: Find all values of x for which ∑ (n=0 to ∞) 1/(1+x)^n equals 4

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Q: Let a, x, and y be real numbers and let e > 0. Suppose that |x-al < e and y-al <e Use the Triangle…

A: Given that, a, x, and y be real numbers and let ε &gt; 0Also,x-a&lt;εand y-a&lt;εWe know…

Q: a) 3x + 1> 2x OR 3x + 1 2x AND 3x + 1 < 5x – 2.

A: 3x+1&gt;2x  or   3x+1&lt;5x-23x-2x&gt;-1 or 1+2&lt;5x-3xx&gt;-1 or  3&lt;2xx&gt;-1 or…

Q: Verify that the sequence g(x) = 5x2 +3 has a fixed point in the interval (0, 1). 11

A: As we know that a point is called a fixed point if it satisfies the equation x=g(x)

Q: Find the smallest integer p so that f(x) = −2x3+8x+2 must have a zero on [0, p] 2,1,5,4, or 3

A: Note: We are not given any particular method. So, we will be solving by the method of graph for…

Q: Estimate to the nearest integer. (Examples 1 and 2) 1. V23 = 2. V197 = 3. V15.6 = Show your work. 4.…

A: Look for the square root of a perfect square near the given number. Which will be the nearest…

Q: The average pollen count in a certain city on day x of the pollen season is  P(x) = 8x − 0.2x2…

A: The average pollen count in a certain city on day x of the pollen season is  Differentiating with…

Q: Determine a constant k such that (kA)" (kA) = 1, where -2 A = Is there more than one value of k that…

A: Given: kATkA=1 A=-21-1

Q: Divide the given interval into n subintervals and list the value of ∆x and the endpoints a0, a1,…

A: Given:           3≤x≤5 ;   n=5 Divide the given interval into n sub intervals Let:       a0=3an=5n=5…

Q: Find the sum of the values of f(x) = x³ over the integers 1, 2, 3, ..., 10.

A: The given function is fx=x3, over the integers 1,2,3.......,10.

Q: Let a, b, and c be real numbers such that a + the maximum value of (ab + bc + ca).

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Q: Q: A- find for the functions: - In =) + In(3x2) = In(3) %3!

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Q: a. Write formulas for length, width, and volume of the box, each in terms of æ . Preview W = Preview…

A: Note: There are many subparts in the question. So I will answer the first subparts in the question.…