Consider a function defined as follows. Given x, the value f(x) is the exponent above the base of 3 that produces x. For example, f(9) = 2 because 3^2 = 9. Evaluate a. f(27) b. f(81) c.f(3) d. f(1/9)

Q: sec 2. Differentiate the following function:

A: Given that  y=sec(5^(-x^2)) To find the differentiation of y

Q: Is there a procedure I can use to write a function as a composition?

A: We can write the innermost function as the last function. And the outermost function as the first…

Q: List the various rules that allow us to differentiate constant functions,power functions,…

A: To explain: The differentiation rule: Explanation: The constant rule is used to differentiate…

Q: If the monthly consumption of water is less the 2800 gallons then $9.48 is charged and if 2801-5500…

A: Given: Amount charged if the monthly consumption of water is less than 2800 gallons = $9.48 Amount…

Q: What is the common way to obtain a new function from an existing one?

A:

Q: Explain how you might differentiate a piecewise function like |x| When it's differentiable, for…

A: We can use the concept of calculus and function in order to solve the given question.

Q: = x3-122 +2

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

Q: Explain in words how to evaluate the derivative of function?

A:

Q: The graph of the first derivative f'(x) of a function f is shown below: 50- -50- 100- Does f have…

A: Given:

Q: FX) = Secx

A: Given function to be differentiated is : F( X ) = sec X2 In order to differentiate above function,…

Q: The graphs of a function f and its derivative f′ are shown on the same set of coordinate axes. Label…

A:

Q: A helicopter is hovering at an altitude of 1,450 feet above sea level.  It descends at a constant…

A:

Q: How to use a graph of a derivative to determine the parent function.

A:

Q: An analysis of passenger traffic at Daytona Beach International Airport over the past 40 years shows…

A: Since you have posted multiple subparts we solved the first three subparts for you To get the…

Q: 5. x²y3 5

A:

Q: When is a function said to have the Intermediate Value Property?

A: Let f(x) be any  function which is continuous and defined in the interval [a, b].

Q: Explain how to graph the derivative of a function given the graph of the function.

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: Suppose f is a function with range (-∞, ∞) and g is a function with domain (0, ¤). Is it possible…

A:

Q: Sketch the graph with details of the function below by using the first and second derivative tests.…

A: We will use following properties of f(x) to draw its graph  # vertical asymptotes are vertical…

Q: Explain how the vertical line test is used to detect functions.

A: Vertical line test: Draw a vertical line on the graph of the given equation. If the line passes…

Q: Differentiate the following function.

A:

Q: Sketch the graphs of two distinct functions with the property f′(x)=−x^2+x

A:

Q: How can looking at the graph of a function help you tell where the function is continuous?

A: For the graph of function to be continuous, it needs to be smooth without any holes, jumps, or…

Q: create a piecewise function showing the rate of money f(x) that must be paid by a customer after…

A: In this question, First, we are to create a piecewise function showing the rate of money f(x)  that…

Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing. show…

A: Topic = Functions

Q: a) f'(-3) where f(x) = 5-3x

A: Derivative using definition

Q: First image is: Is that function diverges or converges? Second image is: Is that function diverges…

A:

Q: Explain Even Functions and Odd Functions?

A: Even function: A function is even if the graph is symmetric about y axis. Or Consider f(x) is any…

Q: Based on past experiences, a homeowner estimates that appliances lose 35% of their resale value each…

A:

Q: How would I find a function that models this?

A: From the given table , it is observed that the given table can represents a linear function.

Q: Please explaune and give exampl of how to use the rule of differentiation to differentiate the…

A: Here the given function Use the rule of differentiation

Q: Is there a function whose graph is symmetric with respect tothe x-axis? Explain.

A: If a graph is symmetric with respect to x-axis for a point (x,y) lying on graph if and only if…

Q: What is the domain of the function that defines the actual distance (in miles), dd, in terms of nn,…

A: Domain is the input value that can be given to a function. The distance on the map varies with the…

Q: Sketch the graph of a function whose derivative satisfies the properties given in the following…

A:

Q: When looking at the graph of an original function, how do you know when the derivative of the…

A: To find the derivative, for your visualization, just draw the graph and the graph of its derivative.…

Q: Sketch a graph of a function whose derivative is always negative. Explain how you found the answer.

A: Sketch a graph of a function whose derivative is always negative. Explain how you found the answer.

Q: The city of New Orleans is located at latitude 30°N. Use Figure 9 to find a function that models the…

A: Given graph, It is clear that the graph is similar to sint where -π2<t<3π2

Q: If electricity is charged every 60 days by Kwh where the first 400 units are charged at a rate of…

A:

Q: Let us try to find where a function is increasing or decreasing given the following. 1. y = 2x –…

A: A function of x is given.We need to find the function is increasing or decreasing in the given…

Q: How can we Represent a Function Numerically?

A: A function f from a set A to a set B is a rule that associates every member of set A a unique member…

Q: Determine the domain and range of the function given to the right. ​(Use interval​ notation)

A: NOTE: Refresh your page if you can't see any equations. . the domain is the set of x-values as we…

Q: 1/3 for

A: Answer

Q: How can we verify the natural domains and associated ranges of some simple functions?

A: let f:X→Y be any function from a non-empty set X to a non-empty set…

Q: What is an even function?

A: we have to tell what is an even function.

Q: Sketch the graph of the function over the indicated interval plot two exact points. y = 2tan( 7x-),…

A: to sketch the graph of the function

Q: of the given function. Explain also the concavity of the point extreme points of the given function…

A: Here, y=2x3-3x2-12x+8. And                y'=2x3-3x2-12x+8' =6x2-6x-12y''=2x3-3x2-12x+8'' =12x-6 For…

Q: Give two examples of functions that are not differentiable.

A: The function is non differentiable at points where limit does not exists or infinite

Q: Determine the domain and range of the function given to the right. (Use interval notation)

A: Domain is the set of x values for which y is defined. Range is the set of y values. The complete…

Q: What is the Horizontal Line Test for One-to-One Functions?

A: we have to define the horizontal line test for One-to-One Functions.

Q: What is the definition of an even function?

A: Let f(x) be a real valued function of a real variable, then f(x) is said to be even function if…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.