3. If x is large, which function grows faster, f(x) = 2* or g(x) = x²?

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: 3. A manufacturer determines that when x thousand units of a particular commodity are produced, the…

A: Given that: Profit function: P(x)=-400x2+6800x-12000

Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

A:

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A:

Q: 1 Is the function given by f(x)= 3x+2, for x ≤ 3, 4x-7, for x>3, continuous at x = 3? Why or why…

A:

Q: Find (f - g)(x) if f(2) = 7x³ – 52² + 42x – 30 and g(z) = 7 O (f · g)(x) = 49zª + 269x² + 150 O (f·…

A:

Q: If f(x) = etan-¹(x²-3) then f'(x) at x = 2 is equal to

A: SOLUTION-

Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: 3. Is the function given by x²-4x-5 -,x< 5 f(x) =. x-5 x+1, x 2 5 continuous atx=5? Why or why not?

A:

Q: 2. Suppose that the marginal revenue for a company manufacturing coffee machines is given by…

A: Given expression for marginal revenue of the company is: Q=100-0.5x where, Q is the marginal revenue…

Q: An article† in The New York Times states, "The number of gas stations [in a city] grows only in…

A: Part (a):To compare the number of gas station.

Q: The U.S. Bureau of the Census prediction for the percentage of the population 65 years and older can…

A:

Q: 5. [ 4 ifx2 Show that f(x) = is not differentiable at x = 2.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the critical points of the function f(x) = 8x^3 + 4x^2 - 12x + 10 and determine their nature.

A: Solution: Given: f(x)=8x3+4x2-12x+10

Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

A:

Q: What are the critical points of the function f(x) = 1

A:

Q: X = (1-_-_-_-)* 2 o then f(x) tend:

A:

Q: 3) State the critical points of the function g(x) = (x – 9) 23

A: A critical point occurs when the derivative is 0 or undefined.

Q: 1 Differentiate f(x) = log, x from the first principle. Note: f'(x) = x In a

A: q- differentiate the function fx=logax from the first principle it is known that, according to first…

Q: Find the critical points of the following function.   f(x) = 1/x - ln(x)

A:

Q: Find the positive critical point of the function f(x) = : 8+6 * x =

A:

Q: What is the length L of the interval on which the function f(x)=x4e−x is increasing?

A: Given

Q: Find the critical points and sketch the graph of the function. 1. f(x) = √5 + x

A: We know that Critical points are points where the function is defined and its derivative is zero or…

Q: Let f(x) = Cx + 7x if x< 4 x³ - cx if x2 4. For what value of the constant c is the function f…

A:

Q: If f (x) = x(x - 2), then the critical points %3D of the function f(x) are

A:

Q: Find all the critical numbers for the function g(x) = % xª -- x3 - 5x?

A:

Q: 4. Suppose that the marginal propensity to consume is dc 0.7-ey (in billions of dollars) dy and that…

A:

Q: If I have f^-1(x)= -x+1 how can I find f(x)?

A:

Q: [4] 2. Find f'(x) using the limit definition of the derivative. Credit will not be given for any…

A:

Q: Find the extreme values of the function f(x)=x√√1- x .- x on the interva

A:

Q: 11. Show that if positive functions f(x) and g(x) grow at the same rate as x→∞, then f = 0(g) and g…

A:

Q: Indicate all critical points of the function f(x)=∣∣x2−5∣∣.

A:

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: fx=lnx,  gx=ln2x

Q: 4. Find the point on the graph of f(x) 5x + 20x – 3 where the tan gent line is horizontal. 5

A:

Q: 3. Give an example of a function with discontinuities at x =1 and x = 5.

A: To Find : A function that has discontinuities at x=1 and x=5.

Q: Suppose a student is a carrier of the flu virus and returns to his isolated campus of 1000 students.…

A:

Q: The rate at which the total average number of COVID cases is increasing at x=10 tents and dxdt=1…

A:

Q: An article† in The New York Times states, "The number of gas stations [in a city] grows only in…

A: Let N be the population in millions and G be the number of gas stations in a city. Given that the…

Q: Find the critical points of the function f(x)=x2lnx.

A: We need to find the critical points of the given function.

Q: [1, 2). over Calculate M6 for f(x) = 3 · In(x³) M6

A:

Q: An article† in The New York Times states, "The number of gas stations [in a city] grows only in…

A: It is give that population is N and G be the number of gas stations in a city related by G=cN0.77.…

Q: The critical points for the 4 function f(x) = x + – is:

A: Given,          The function is fx=x+4x .

Q: Suppose that the marginal revenue for a company manufacturing coffee machines is given by 100−0.5x…

A:

Q: 4. Use the limit definition of derivative to find f'(x) for f(x) = V5x + 1. You will only get credit…

A:

Q: 4. By the definition of derivative prove that f(x) = √x² +5 is differen- tiable at x=2.

A:

Q: Suppose that the function f(x) is concave down on the interval (2,5). Can conclude that the function…

A:

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Using the product rule of natural logarithm, it can be written that ln(ab)=ln(a)+ln(b) . Using the…

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: Use limit methods to determine which of the two given functions grows faster, or state that they…

Q: Rank the functions x100, ln x10, xx, and 10x in order of increasinggrowth rates as x→ ∞.

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.