. Let f(x) = { 3x, x > 1                           { x^3, x < 1  Sketch the graph of f. Is it possible to find a value k such that f(1)=k, which makes f(x) continuous for all real numbers? Briefly explain.

Q: 3. Determine f(x) = x2 + x-2 is continuous on the given interval (-0,+0) (show graph and its table…

A: Here, the given function is: f(x)=x2+x-2 And the given interval is (-∞,∞).

Q: 2. When can we say that a function is continuous at an interval?

A: We know that when a function does not have any discontinuity, then it is a continuous function. It…

Q: Determine the value of the constant a for which the function f(x) is continuous at -4. x + 7x + 12 x…

A: Given function is fx=x2+7x+12x+4 if x≠-4a                  if x=-4 We have to find the value of a.…

Q: 1. How to determine whether the function is continuous or not at a certain point?

A: As per our guideline we are supposed to be answer only one question please repost the other question…

Q: 1. Find the numbers for x where the function below is not continuous. Explain what type of…

A: Here the given graph

Q: On which interval is the function f(x) = tan x² continuous Is the function f(x) = ! - continuous at…

A: 3.1)  tan x2 =sin x2cos x2We know that sin x2 and cos x2  are both continuous functions.Thus, tan…

Q: The graph of the derivative f' of a continuous function f is shown. (Assume the function f is…

A: Given that: Graph of f'(x)     NOTE: As per our answering guidelines, we can only answer 1 question…

Q: 67. Is the function given by g(x) 1 continuous over %3D x + 5 the interval (-4, 4)? Why or why not?

A: g(x)=1x+5

Q: 3. Determine f(x) = x +x-2 is continuous on the given interval (-0,+0) (show graph and its table of…

A:

Q: 1. What is the definition of what it means for f(x) to be continuous at x = a? Discuss the ways that…

A: In this question, we need to define the meaning of f(x) to be continuous at x=a and different ways…

Q: Give an example of a function ƒ(x) that is continuous for all values of x except x = 2, where it has…

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 for a function to be continuous on an interval? Give examples to illustrate the…

A: In simple terms, if the graph of a function can be drawn without lifting the pen from the paper, we…

Q: Explain the differences between continuity and uniform continuity when f(x)=2x+1 shown on graph…

A: According to definition of continuity and uniform continuity, they are differ depending on the ε and…

Q: Determine where the following function is continuous. X- 1 M(x) = 9x2. - 16 The function is…

A:

Q: explain the mathemahcal definition of continuily at x=3. Use sentences or math expressions in…

A:

Q: 81. A function y = f(x) is increasing on the interval (0,5). What conclusions can you draw about the…

A: If a function is an increasing function then this means when the value of the variable x increases…

Q: (a) What does it mean for f to be continuous at a?(b) What does it mean for f to be continuous on…

A: a) What does it mean for f to be continuous at ab) What does it mean for f to be continuous on the…

Q: 1. Find the numbers for x where the function below is not continuous. Explain what type of…

A:

Q: Find the absolute extreme values of the function on the interval f(x)=tanx, -pie/6 less than or…

A: To find the extreme values of the function on the interval, f(x)=tanx, -π6≤x≤π6

Q: Find the points at which the function f (x) is continuous and the points at which f is…

A:

Q: Come up with an example of a continuous on [0, 2] function for which the trapezoidal rule is more…

A: Let us consider a continuous function fx=cosx for x∈0,2. fx is continuous on 0,2 Now, exact value of…

Q: fully continuous for all x E R by use of the product rule differentiate the function f{x} = x3e-4x

A:

Q: Determine where the following function is continuous. x-1 M(x) = 4x²-81 The function is continuous…

A:

Q: 9. Sketch a graph that has the following properties: (i) ƒ is continuous on (-∞, ). (ii) f'(x) 0 on…

A:

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

A:

Q: 5. Sketch a graph off given the following conditions: - Continuous on intervals (-∞, -3), [–3, 2)…

A: To sketch the graph habing all the properties . If right hand limit is not equal to left hand limit…

Q: Suppose f is a continuous function on [a,b] and suppose that f(a) 0 What can you say about the…

A:

Q: Determine whether the function is continuous at the given points. x+2 if x22 : 2,0 x if x<2 f(x) =…

A:

Q: How would you define f(2) in order to make f continuous at 2? limx→2 x^3-8/x^2-4 show ALL of your…

A: Let's solve limit problem.

Q: 28. Use the limit definition, lim 7 (x+h)- f(x) to determine the derivative of x-1. [Value of 4] h0

A:

Q: Q.3: Discuss the limit of f (x) = - at x = 0¬, 0*,-∞, +∞, with graphs. %3D

A:

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: Suppose f is continuous on the interval (0,3). Assume further that f(0)= -2 and f(-3)= 5. Also, lim…

A:

Q: Find f'(x). f(x) = x° – 4x³ + x – 1 - f'(x) = Compare the graphs of f and f'and use them to explain…

A: NOTE: Refresh your page if you can't see any equations.     . take derivative

Q: The table below gives for the value of continuous function f at each x-value. Using the Intermediate…

A:

Q: 10) Demonstrate with graphs even and odd functions. Identify the functions.. Even function: f(-x) =…

A: Graph even functions: In very simple words even function are functions having symmetry about the…

Q: Determine the value of the constant a for which the function f(x) is continuous at - 3. x2 + 8x + 15…

A:

Q: sketch the graph of a function that is continuous everywhere except at x=3, and is continuous from…

A:

Q: 25. Let f(x) be a continuous function. Express + ()] lim п—оо as a definite integral.

A: Definite integral in the form of the limit of the Riemann sum:   Let f(x) is a continuous function…

Q: 2. Sketch a graph of a function f that is continuous on (-00, 00) and has the following properties.…

A:

Q: Sketch a graph of the function f that is continuous on (- 00,00) and has the following properties.…

A: Given, Graph of the function f(x) is continuous on-∞,∞ y=f(x) and has the following…

Q: 2) Use the definition of the derivative f(x+h)-f(x) lim hー→0 to find the derivative of f(x) =…

A: Our objective is to find the derivative using definition.

Q: 2. Sketch a graph of each function described. A. A function that is continuous everywhere except at…

A: Note:- As per our guidelines, we can answer the first three sub-parts of this problem as exactly…

Q: Come up with an example of a continuous on [0, 2] function for which the trapezoidal rule is more…

A:

Q: (x + 1, x 0 Can also be displayed as: x + 1 when x 0 f(x) = Is f(x) continuous at x = 0? Why or why…

A: We have to find the solution of continuity

Q: Sketch a function that is continuous on (- 00,00) and has the following properties. Use a number…

A: →Let y = f(x) be any function.   When, f'(x)&gt;0 then function is increasing.   When, f'(x)&lt;0…

Q: x' - 8 24. f(x) : x? – 4

A:

Q: a function is continuous at x = c, then the limit exists as x approaches c. If the domain of a…

A: a. If a function is continuous at x = c, then the limit exists as x approaches c By the definition…

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.