Demonstrate that f(n) = log n! is bounded below by O(nlog n).

Q: xplain why F, contains a primitive nth root of unity if and only if p = 1 mod n. int: Use the…

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Q: show that is strictly increasing or strictly decreasing. n=1

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Q: Give an example of a sequence of real numbers {xn}® such that its limitpoint set is just the set of…

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Q: Consider the function f(x) = 7x – 6x? – 2. Identify the locations where f has transition points, the…

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Q: Find the asymptotes, intervals of increase, decrease, concave upward, concave downward, local max,…

A: No asymptotes, Increasing when X<3/4 Decreasing when 3/4<X<1 Concave down for x<1 Local…

Q: Identify the open intervals where the function f(x) = 4x+ 4x+ 1 is increasing or decreasing. a)…

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Q: Let f be a function that is positive and differentiable on the entire real number line and let g(x)…

A: Given: f(x) >0 , f is differentiable on the entire real line  and g(x) =ln(f(x)) g is increasing.

Q: (b) Find the big O of the function f(n) = n²" + n"

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Q: 6. True or False The cube function is odd and is increasing on the interval (-o, ).

A: True We know that, A function f is said to be odd if f(-x)=-f(x) We have a cube function that is…

Q: Identify the intervals where Increasing O (-1, 3) O (-2, 1) O (-2, -1) or (3, ) O (-1, 0)

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Q: Find all intervals where f is decreasing.

A: Given,           f(x) =6x2 + 2x - 19

Q: Determine all intervals on which f(x) 2 0. Graph of f 8. 6. 5. 4 3. -9 -8 -7 -6 -5 -4 -3 3 4 5 6 78…

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Q: uppose f() is a polýnomial with three zeros: 3 of multiplicity 1, - 2 of multiplicity 2, and a zero…

A: Given:- Suppose f(x) is a polynomial with three zeros: a zero at x= 3 of multiplicity 1, a zero at…

Q: Find the o symptote s func tion given of the below f (x)= 2-5x+3 メ-2

A: We need to find the asymptotes of the given function.

Q: 5. Find the domain off(z-In(e*-3). Then find f-1 and its domain.

A: f(x) = ln(ex-3)The function "ln" is defined for positive numbers only.Hence, x should be such that…

Q: Give the domain of s(x)=x2+2x√16−5xs(x)=x2+2x16-5x in interval notation

A: Given the functions(x)=x2+2x16−5x

Q: Show that every increasing function is one-to-one.

A: A function f from A to B is called one-to-one (or 1-1) if whenever f (a) = f (b) then a = b. No…

Q: Show that increasing functions are one-to-one. Then show that                              f(x) = x…

A: To show that  f(x) = x 5 + 4x + 3 is one-to-one. A function is said to be one-to-one if for…

Q: True or False Every polynomial function is continuous atevery real number.

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Q: Find the open intervals where ƒ is increasing or decreasing.

A: To find the  open intervals where ƒ is increasing or decreasing. Given that the function is…

Q: Prove f:N - N. F(X) = 5x is injoctive.

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Q: b) Find the intervals on which fis decreasing

A: The graph is drawn with a scale of 1 unit on x-axis and y-axis.

Q: Select all the intervals where g is decreasing.

A: Given data: The given graph of the curve g(x) is shown in the problem. By looking at the graph the…

Q: Find the open intervals where f is increasing or decreasing. f(X)= 10 - x + x2

A: we have to find the intervals where f(x) is increasing or decreasing. f(x)= 10 - x + x2

Q: x : x is a natural number less than 10​}

A: Write in explicit form

Q: If $500 is deposited in a bank account paying 3.5% interest com- pounded monthly, then the account…

A: VN=5001+0.03512N The graph is,

Q: Select all the intervals where f is increasing. 2.5+ y= f(x}- 2+ 1.5+ 1+ 0.5- -4 -3 -2 -1 3 4 -0.5+…

A: Consider the given graph. We have to find the all the intervals where f is increasing. Definition of…

Q: Suppose a increases on

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Q: 14) Show that f (æ) = -æ³ +2 is decreasing on the entire real number line. (Show Graph)

A: we have to show that the given function is decreasing and also draw the graph of f(x)

Q: Describe how the greatest integer function is continuous at every real number other than the…

A: Given- A greatest integer function. To show- how the greatest integer function is continuous at…

Q: Let f(x) -2x² + x-5. Find f(-x). f is -- O odd O Even Neither All of the above

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Q: Q1) Determine the halve range odd expansion of the function whose definition is: 0≤x≤1 f(x) = - {...…

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Q: 13. Which recursively defined function has a first term equal to 10 and a common difference of 4?…

A: The function has first term equal to 10 and a common difference of 4

Q: Show that E( X - K )2 = var( X) + [E(X) - K]2

A: var(X)=E(X2)-E(X)2 E(a)=a  where a is constant (a-b)2=a2-2ab+b2

Q: if n 3 a1 = a2

A: We will get the corresponding term by putting value of n in the given constraints.

Q: Alice is in a 20-km running race. She always runs the first half at an average speed of 2 km/h…

A: Alice is in a 20-km running race.She always runs the first half at an average speed of 2km/h faster…

Q: Pr ove that the set of all open intervals with rational end points is a base for the usual topo log…

A: We have to prove that the set of all open intervals with rational end points is a base for the usual…

Q: A store had 50 bottles of olive oil. Each week, 40% of the olive oil bottles were sold and 20 new…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Find the intervals on which ƒ is increasing and the intervals on which it is decreasing. ƒ(x) = 4 -…

A: Given, fx=4-x2

Q: Throughout which intervals is f(x)=2x³ 3x2-12x increasing? -00 < x < -1 -1< x < 2 -2 < x < 0 - -20 <…

A: The function is given by fx = 2x3-3x2-12x To evaluate : The interval where the function is…

Q: On which intervals is the funcrion increasing and decreasing?

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Q: 5. T(n)= 3T (%) +2n base case: n = 1

A: Solution:

Q: Which of the following tables represents an exponential functic f(x) -1 1/3 f(x) -1 -3 -3 2 -12 f(x)…

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Q: From the graph of f, indicate the intervals on which f is continuous. 6+ 2+ -6 -2 -2+ 4+ O (-00, 2]…

A: Your second option is correct ...at x=2 graph is discontinuous so in the interval x=2 is…

Q: Construct a formula for the volume of the resulting box. What’sthe domain of the function? What’s…

A: From the given, the dimesion of the cardboard is observed to be 30 inches by 40 inches. And each of…

Q: find the positive intervals for  x2 − 3x

A: We need to find the interval for which function is positive .

Q: Determine all intervals on which the graph of J is decreasing. Graph of f 8 4 3 -9 -8 -7 -6 -5 -4 -3…

A: According to given graph it is decreasing in x∈-∞,-4∪-1,5

Q: Use the graph to determine 1- a. open intervals on which the function is increasing, if any. b. open…

A: Given, The graph of the function  We have to find the intervals in which function is increasing,…

Q: the domain cant be x >3? its a union of intervals?????

A: fx=-3x+1 and gx=x-3

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.