Suppose than an object that is originally at room temperature of 30 Celsius is placed in a freezer. The temperature T (x) of the object can be approximated by the model T (x) = 360 / xˆ2 + 4x + 12, where x is the time in hours after the object is placed in the freezer. a) What is the horizontal asymptote of the graph of this function and what does it represent in the context of this problem? b) A chemist needs a compound cooled to less than 5 Celsius. Determine the amount of time required for the compound to cool so that its temperature is less than 5 Celsius.   PLEASE DO NOT USE LIMIT TO SOLVE IT.......I CAN NOT USE LIMIT IN THIS CLASS.

Q: Find the horizontal asymptotes of the function by computing the limits at infinity.

A:

Q: The graph of f(x)=(1.68)xf(x)=(1.68)x is shifted right 33 units, stretched vertically by a factor of…

A: The given function is fx=1.68x. shift right 3 units, stretched vertically by a factor of 2. Then…

Q: The graph of the function fx) =/x is stretched vertically by a factor the transformed function…

A: Given- The graph of the function fx = x is stretched vertically by a factor of a and is translated 3…

Q: What is the process for determining the horizontal asymptote of a function from its equation?

A: The method used to find the horizontal asymptote changes depending on how the degrees of the…

Q: True or False: A vertical asymptote and a hole in the graph create places of discontinuity that…

A: If there is a vertical asymptote or a hole in the graph of function then there must be discountunity…

Q: Given the two functions, explain how the characteristics (Zeros, Vertical Asymptotes, Horizontal…

A: for vertical asymptotes, put denominator=0 and for zeroes, put y=0

Q: Suppose you are given a formula for a function fpxq, and you are asked to find all the critical…

A: Suppose, Given - a formula for a function f(x) Critical Points: Critical point of a function are the…

Q: Sketch the graph of each function. Indicate where each func- tion is increasing or decreasing, where…

A: We’ll answer the first question (that is 23) since the exact one wasn’t specified. Please submit a…

Q: ASYMPTOTE

A:

Q: What does it mean for the graph of a function to have a horizontal asymptote?

A:

Q: Find any asymptotes and relative extrema that may exist and use a graphing utility to graph the…

A:

Q: Find the horizontal asymptotes of the function by computing the limits at infinity.

A: Asymptote is a line along which the function tends to infinity or minus infinity. Horizontal…

Q: What is the horizontal asymptote of the function n(X) x +1

A:

Q: find the horizontal asymptotes of the function by computing the limits at infinity.

A: Find the limits at infinity,

Q: ) Suppose we shift the graph of f vertically downwards by h units such that the maximum turning…

A: Given, the function f and g are defined by              f(x)=acosk(t-b)and              g(x)=mcsc…

Q: How is the graph of the entire function different from the graph for the real-life situation?  2)…

A: Answer for sub question 1; Given Cn=600+115nn Then, C'n=-1n2600+115n+1n115=-600n2-115n+115n=-600n2…

Q: what is the graph of the following function (2x+1)(x+2)/(x-1)(x-3)?  where are it's vertical and…

A: The objective is to draw the graph and find vertical and horizontal assymptote.

Q: Suppose a cannon is placed at the origin and elevated at an angle of 60 degrees. If the cannonball…

A:

Q: How can you determine from the equation of a function if it has a vertical as- ymptote or a hole…

A: We have to explain how to determine the vertical asymptote and hole of the given function.

Q: Suppose a cannon is placed at the origin and elevated at an angle of 60 degrees. If the cannonball…

A:

Q: Find any asymptotes and relative extrema that may exist and use a graphing utility to graph the…

A: The function is y=lnxx. The vertical asymptote occurs at the points where the function becomes…

Q: Write down a function that has vertical asymptotes at the points x=1, x=2, and x=3, and a horizontal…

A: Given The function has vertical asymptotes at the points x=1, x=2, and x=3, and a horizontal…

Q: Find any asymptotes and relative extrema that may exist and use a graphing utility to graph the…

A: The relative extrema is obtained when the first derivative of the function y=lnxx equals zero. The…

Q: A function has a y-intercept of 2 and is increasing for values of the domain greater than 4. Which…

A:

Q: Find the points on the graph of f(x) = 2x3 + 15x2 - 84x + 12 where the tangent is horizontal. List…

A: we have to find the points on the graph of the function f(x) = 2x3 + 15x2 - 84x + 12 where the…

Q: The function f  whose graph is given has a discontinuity at x=4 since  does not exist. Prove true…

A: Topic:- function

Q: How can we analyze the graphs of functions having horizontal or vertical asymptotes?

A: Check for when we have vertical and horizontal asymptote

Q: The hypotenuse of an isosceles right triangle is to be made into a circle C. Express the area A of C…

A:

Q: Create a function f(x) in standard form with an oblique asymptote at g(x) = - x +4, hole at x = 2, a…

A: Use the following definitions, to obtain the required result. The vertical asymptote occurs when…

Q: Given the function g(x) = 8x³ + 12² – 48x, find the first derivative, g' (x). g'(x) = Notice that…

A: We can solve this as follows:

Q: find all vertical and horizontal asymptotes algerbraically, f(x)=3x^2-x+5/x^2-4

A: . Find all vertical and horizontal asymptotes algebraically, f(x)=3x^2-x+5/x^2-4For calculating the…

Q: Suppose a cannon is placed at the origin and elevated at an angle of 60 degrees. If the cannonball…

A:

Q: How many asymptotes does the function Ax) = x-1 (x+ 1) have?

A:

Q: A manufacturer finds that the revenue generated by selling x units of a certain commodity is given…

A:

Q: Plot the graph of f (x) = x/(4 − x) in a viewing rectangle that clearly displays the vertical and…

A: Given, f(x) = x/(4 − x) 1. Vertical asymptote. Since the denominator of the fraction is (4 − x),…

Q: Determine from the graph whether the function has any absolute extreme values on [a, b]. Then…

A: For given graph, Absolute Maximum is at x = d. and  Absolute minimum does not exist.

Q: The graph of y= f(x)= √x-9 is horizontally stretched away from the y-axis by a factor of 3 to…

A:

Q: At what x value does the local maximum occur for the function x^3 -4x-2 ? Give your answer in…

A: It is maximum value problem.

Q: The graph of f has a point of inflection at x=5 but this is also a vertical asymptote. Can the graph…

A: For x = 5 to be the point of inflection the concavity must change. This can be done only in these…

Q: What are the end-behavior asymptotes for the function f (x) = ? 2z+1

A:

Q: y = + x2 (х — 2)2

A: Given

Q: What are the vertical and horizontal asymptotes for the function f(x)= 6x^2+x/x+1

A: To find the vertical and horizontal asymptotes for the function f(x)= 6x^2+x/x+1

Q: How can you determine from the equation of a function if it has a vertical asymptote or a hole…

A: First of all we rearrange the given equation of function as rational function. Then factor the…

Q: Investigate the connections between key properties such as increasing/decreasing intervals, local…

A:

Q: .An x by x square is cut from each corne of a rectangular sheet of cardboard tha is 8 inches wide…

A:

Q: Sketch the graph of y = (x² – 2)² – x². [In your answer, you must include the following: • Find the…

A: We have to sketch the graph of function y=x2-22-x2

Q: The point (0, 1) is not a point on the curve, due to the fact that division by zero is not - This is…

A: Given function, f(x)=sinxx over domain [-2,2]

Q: What are the horizontal asymptote and y-intercept for the graph of this function f(x)=2-x+7 ?

A: Given function