Give an example to explore numerically how a function behaves near a particular point at which we cannot directly evaluate the function?

Q: Is there a function that is both even and odd?

A: Yes, f(x)=0 is both even and odd.

Q: 2. what is the domain of the function)

A: Given function is, f(x,y)=cos-1x2+y2-3+lnx2+y2-3 The graph of the function is,

Q: 8. Determine algebraically if the function is even, odd or neither. y = -2' - |-2°|

A:

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

A:

Q: Give a geometrical interpretation of the function In x

A: To give: Geometric interpretation of the function ln x=∫1xdtt. Concept used: The area under the…

Q: Make a function that violates Clairault's Theorem. Explain why it does. Show how you got it.

A:

Q: Sketch a rough graph of the function without using acalculator.   y=   In (x  -1 )

A:

Q: Describe the behavior of a function when the magnitude of the independent variable x becomes…

A: End behaviour of a function: The end behaviour of a function 'f' describes the behaviour of the…

Q: 10. Identify three characteristics to the graphed function of f (x) = (÷) +1.

A:

Q: 3) Without a graph, how can one show differentiability of a function at apoint?

A: With out the graph, to show the differentiablity of a function at a point we have to use the…

Q: 1. What is an appropriate domain for the function? Explain how you know.

A: The domain of any function f(x) is the set of all values of x for which the function is defined.

Q: so if|x| 2 43. f(x)

A: Following is the graph plotted for individual functions.

Q: sketch to graph the function f(x) = In(x + 2) – 1. %3D

A: f(x)=ln(x+2)-1Now, putting value of x=-1f(-1) =ln(-1+2)-1           [ln1=0]           =0-1…

Q: How can the composite function be evaluated?

A: To explain how the composite function can be evaluated.

Q: The graph of a function is shown below. On which interval is the function increasing and non-linear?

A:

Q: How do you test a twice-differentiable function to determine where its graph is concave up or…

A: According to the Second Derivative Test for Concavity, Consider y=fx be a twice-differentiable…

Q: How does  a function behave near a particular point at which we cannotdirectly evaluate the…

A: To understand the concept we will consider an example

Q: Write an equation that expresses the fact that a function f is  continuous at the number 4.

A:

Q: Determine all of the relative extreme values of the function f (x) = 1 – (x – 2)- %3D

A:

Q: This describe the value of a function as approaches to some value?

A: Since we know that limit of a function f(x) as x approach c, f(x) approaches x as approaches c.

Q: Which of the following is not a function in implicit form?

A: A function is in implicit form when f(x,y)=0 and explicit function is y=f(x).

Q: Identify the open intervals where the function is changing as requested. Decreasing

A: We have to find the interval where the function is decreasing.

Q: Use the graph of the function to estimate the interval on which the function is decreasing.

A: A function is said to be increasing when the y value increases as the x value increases.

Q: Draw the graph of any function f (x) that passes through the point (3, 2).

A: Consider the function  f(x)=x-1. Put x=3. f(3)=3-1=2. So the graph of the function passes through…

Q: What is the domain of this function?

A:

Q: Outline a method for locating the relative extreme points of a function.

A:

Q: When is a function of two (three) independent variables continu-ous at a point in its domain? Give…

A:

Q: Is it possible for a function f to attain only positive values (that is, f(x) > 0 for all x) and…

A:

Q: What do all members of the family of linear functions f(x)=  c- xhave in common? Sketch several…

A: Given :           fx=c-x

Q: 1. What is an inflection point and how do you identify it? 2. How do you test a function to be…

A: Note: In Case of multiple questions, as per the guidelines answer to first question will be…

Q: What is an appropriate domain for this function?

A:

Q: About the Discontinuity of a function, kindly provide 5 Questions about it with solutions.

A: For a function f(x) to be continuous at a point x=a, it must satisfy the two of the following…

Q: Describe how to tell when a function is discontinuous at thereal number x = a.

A: There are three conditions that need to be satisfied by a function f(x) in order to be continuous at…

Q: Identify the intervals for which the function is increasing / decreasing.

A:

Q: How can the One-to-One Functions Graphically be identified?

A: If a function has no two ordered pairs with different first coordinates and the same second…

Q: A function is even if the opposite input results in an

A: For even function :f(-x)=f(x)

Q: How to find the derivite of a function?

A: To explain how to find derivative of function:

Q: When is it possible to compose one function with another? Give examples of compositions and their…

A: A new function can be created by combining the two pre-exist functions. This new function can be…

Q: f (z) = 2

A:

Q: Explain thoroughly and illustrate what it means for a function to be differentiable at a number a

A: First we will give the definition of a differentiable function then we will illustrate it with an…

Q: What are even and odd functions of symmetry? For example f(-x)=-f(x), f(-x)=f(x), Symmetric about…

A:

Q: Give 1 example of real life situational that involves determining the function model in peicewise…

A: In day to life taxi fares are a piecewise constant function of distance traveled The rate of income…

Q: How can a function be described in pieces?

A: A function can be described in pieces with different formula in different intervals of its domain.

Q: What are the important types of functions frequently encountered in calculus? Give an example of…

A: Some of the important functions encountered in calculus with examples are as follows.

Q: The original and restricted functions are not the same functions.True or false?

A: Given, 'The original and restricted functions are not the same functions.

Q: he critical points of the function f(:

A: Find the critical points of the function  f(x)=6x2-12x

Q: Construct a function that is undefined at points 2,3 and π

A: We have to write a function fx which is not defined at the points x=2, x=3 and x=π. We know that a…

Q: Give Definition of Even Function ?

A: A function fx is said to be the even function if it satisfies the condition as, f-x=fx, for any…

Q: What conditions have to be checked to determine if a function is "well defined"?  How would I show…

A: Let the function beThen we need to check 3 conditions to prove that the function is Well definedThey…

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.