Explain why each function is continuous or discontinuous.(a) The temperature at a specific location as a function oftime(b) The temperature at a specific time as a function of thedistance due west from New York City(c) The altitude above sea level as a function of the distancedue west from New York City(d) The cost of a taxi ride as a function of the distancetraveled(e) The current in the circuit for the lights in a room as afunction of time

Q: Find all points where the function is discontinuous.

A: Function is discontinuous at points where graph breaks. So, we have to find point where the given…

Q: What does it mean for a function to be continuous on an interval?

A: A function is said to be continuous on the interval when the function is defined on every point of…

Q: The owner of a luxury motor yacht that sails among the 4,000 Greek islands charges $470 per person…

A: Let the number of passenger above 20 be xthen the cost per passenger = 470 - 5x

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

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

Q: Express the area A of an isosceles right triangle as a function of the length x of one of the two…

A: We have to express the area A of an isosceles right triangle   We have to write area as a function…

Q: Find the intervals on which the function y=xx(x>0) is increasing and decreasing.

A: We take ln on both sides of the function

Q: List the  Properties of Continuous Functions?

A: given,       List the  Properties of Continuous Functions

Q: What is the domain of the secant function?

A: Secant function , Sec xWe know        Sec x=1cos xTo find domain Put cos x=0

Q: What does it mean for a function to be differentiable on an open interval? On a closed interval?

A: If a function f is differentiable on an open interval (a,b) then it means that the function is…

Q: Please illustrate the difference between a function being continuous and differentiable by…

A: We have to  illustrate the difference between a function being continuous and differentiable…

Q: 4. List the discontinuities for the function f(x) = cot(* :).

A: First write the given function into Numerator and denominator form and , to find the discontinuity…

Q: y -2

A:

Q: 85. Suppose that f is the differentiable function show panying graph and that the position at time t…

A:

Q: What does it mean if a function f is increasing on an interval?

A: Let the given function be y = f(x) And the interval be I.

Q: What does it mean for a function to be right-continuous at a point?

A: A function f is right continuous at a point c if it is defined on an interval [c, d] lying to the…

Q: Determine the intervals on which the function is continuous. %3!

A: To find: The interval in which the function fx=12-x is continuous. Concept used: The domain of the…

Q: Describe the intervals on which the function is continuous.

A: Discuss the interval on which the function is continuous

Q: A pebble is embedded in the tread of a rotating bicycle  wheel of diameter 60cm. If the wheel…

A:

Q: Determine whether the function is continuous or discontinuous 5. f(x) =

A:

Q: If a function is differentiable at a point, then it is continuous at that point. A) True B) False

A:

Q: On which interval is the function f)= -x- increasing?

A:

Q: b) State what it means for a function to be continuous at a point x = a.

A:

Q: 1) If possible, give an example of where a function is differentiable at a point but not continuous…

A:

Q: Describe the intervals on which the function is continuous.

A:

Q: = Find a continuous function

A:

Q: 3. Sketch the graph of a function that is continuous, but not differentiable at I= 1.

A:

Q: A pool measuring 20 meters by 10 meters is surrounded by a path of uniform width, as shown in the…

A: Given information: A pool of rectangle size of length 20 m and breadth 10 m, Surrounded by a path of…

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

A: When is a function of two (three) independent variables continuousat a point in its domain? Give…

Q: When is a function periodic?

A: A function is periodic if there exists a positive real number M such that, fx+M=fx The smallest…

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

A:

Q: A wire of length x is bent into the shape of a circle.(a) Express the circumference C of the circle…

A: Given: A wire of length x is bent into the shape of a circle.

Q: A tortoise and a hare are competing in a 1200-meter race. The arrogant hare decides to let the…

A: Given A tortoise and a hare are competing in a 1200-meter race Tortoise has a 750 meter head start…

Q: Describe the intervals on which the function is continuous.

A:

Q: A closed rectangular box with a square base has a volume of 8000 cubic centimeters. Express the…

A:

Q: When can we say that a function is continuous at a number?

A: To explain: The continuity of a function at a point.

Q: V16-x2 f(x) = at (-3,-1) x+1

A: Given function is fx=16-x2x+1 The interval is -3,-1 We know that function is continuous in any…

Q: In your own words, describe what it means for a function to be continuous at a poin

A: A function is called continuous when graph of function is continuous or does not broken in its…

Q: What does it mean for a function to be continuous on an interval?Give examples to illustrate the…

A: For open intervalIf f:(a, b)→ℝ is defined on an open interval, then f is continuous on (a, b) if and…

Q: Which derivative of f tells us whether the function is increasing or decreasing?What do we check to…

A: Given function ,  f(x) = ln ( x2 + 2x + 5)  Find interval of increasing and decreasing .

Q: Determine the intervals on which the function is concave upward and/or downward.

A: We will use second derivative test for concavity

Q: Is the function continuous or discontinuous? If discontinuous, what condition is not satisfied?

A: Given:

Q: Is the function continuous or not? If not, what condition is not satisfied? Present solution

A: A function fx is said to be continuous at a point at x=c if 1. fc is defined and exists 2.…

Q: State the intervals on which the function f is continuous

A: A function is said to be in an interval if it's graph runs continuously without any break it that…

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

A:

Q: In calculus was claimed  that increasing (or decreasing ) functions  defined on a single interval is…

A: Consider a one - to - one function in an fixed interval.  For the function f(x), in the interval 0…

Q: why the function is continuous at every number in its domain. State the domain.

A:

Q: Describe the intervals on which the function is continuous.

A:

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.