4. Explain what it means for a function f to be continuous at a point x = c, with a sentence that includes the words "approaches" and "value."

Q: Is the function f graphed below is continuous at = -4? Choose the appropriate reason that justifies…

A: topic - continuity and limits f is not continuous at x =-4 reason = left hand limit is not equal to…

Q: Determine the discontinuities of the following functions and state why the function fails to be…

A: f(x)=x3+x2-17x+15x2+2x-15function is undefine when x2+2x-15 is become 0Let…

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: Assume whether the function graphed in the accompanying figure is continuous on [-1,3]. y = k(x) 2 3…

A: for being a contrinuous function this condition should be satisfiedlimx→a-f(x)=limx→a+f(x)=f(a)from…

Q: Consider the following. Find the x-values at which f is not continuous. Which of the discontinuities…

A:

Q: Use the graph to answer the question. Is f continuous at x = 0? %3D -4- -5- 2.

A:

Q: Explain, using the theorems, why the function Is continuous at every number In Its domaln. x- 9 Q(x)…

A: Given: Q(x)=x-93x3-9 To find: The domain and Why the function is continuous at every number in its…

Q: The function is discontinuous at x= -4. At this point, is f continuous from the right, left, or…

A: A function f is said to be right continuous at a point a if it is defined on an interval and if…

Q: x2 – 1 f (x) ; x = 1 х — 1

A: We will solve the following

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: 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: For function f, how would you remove the discontinuity? In other words, how would you define f(5) in…

A: For continuity limit of function at a point should be equal to functional value at that point.

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

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

Q: 71. Is the function given by g(x) = 4x - 6x continuous on R?

A: To check whether the function g(x) is continuous on ℝ. The given function is gx=4x3-6x Also, the…

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: say whether the function graphed is continuous on[-1, 3]. If not, where does it fail to be…

A: It is clear from the graph that  function y=g(x) is continuous in [-1,3) But at x=3, Therefore, g…

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

A:

Q: Is the following function continuous at x = 2? Explain why or why not. x2 +x – 6 - :x > 2 f(x) = x –…

A:

Q: Explain if the function is continuous or not for the given number a. if x > 1 f(x) = {1 if x = 1…

A: topic - limits and continuity

Q: In The given question, , determine whether the statement is true or false. If it is false, explain…

A: we have to tell whether the given statement is true or false. Statement : If a function is…

Q: (x – 2)2 +1 if x 2

A: We have to check continuity of function at x=0 and x=2

Q: Which of the following functions are continuous? Why do you think they are continuous?

A:

Q: (b) Redefine f(4) so that f is continuous at x = 4 (and thus the discontinuity is "removed"). f(4) =

A: The given function is: f(x)=x2-12x+32x-4

Q: State both the converse and the contrapositive of the assertion “Every differentiable function is…

A: We will make use of fundamental definition of these terms.

Q: Determine using the given graph if the function f is continuous on the following intervals. 1. a.…

A: A real valued function f(x) is defined in an interval,say [a,b] and its graph is available to…

Q: Determine whether the following function is continuous at a. f(x) = /x- 7; a = 1

A: Topic :- Continuity

Q: Is the functionf graphed below is continuous at x= -1? Choose the appropriate reason that justifies…

A: Continuous at x=-1, as limit is equal to f(-1).

Q: Suppose that (picture) If f is  continuous for all real numbers, then c is equal to:

A:

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

A:

Q: what is the mathematical condition for the function to be continuous at a certain point c?  is the…

A: A  function is said to be comtiuous at a point x=c , in its domain if the following three conditions…

Q: Suppose fx) is a continuous function. Then a function F(x) Such that F'(x) =f{x) is called:

A: Given:- Suppose f(x) is a continuous function Then a function F(x) F'(x) = f(x) is called

Q: Determine the discontinuities of the following functions and state why the function fails to be…

A:

Q: 1. Write the conditions a function has to meet in order to be continuous at point a. a) b)

A: A function f(x) has to meet these conditions in order to be continuous at any point a

Q: Determine algebraically if f is continuous at x= 0.

A:

Q: Graph h and describe the discontinuity: h(x) = { ex lnx for x < 0 for x > 0 Is h left- or…

A: Given the function h(x)=ex lnx.  We need to sketch the graph for the given function for x<0 and…

Q: Graph h and describe the discontinuity: for x 0 Is h left- or right-continuous?

A:

Q: Recall from calculus, if a function is differentiable at a point c, then it is continuous at c, but…

A:

Q: Determine whether the function is continuous at the given points. x+30 if x26 6, 0 if x <6 f(x) = Is…

A: Solution

Q: For the function f, how would you remove the discontinuity? In other words, how would you define…

A:

Q: Is f continuous at x = 2?

A:

Q: Which of the following is a function that has a jump discontinuity at x = 2 and a removable…

A:

Q: What can be said about f (3) if f is continuous andlim f(x) = ½? x→ 3

A: Given that, the function f(x) is continuous and limx→3fx=12. Since, function f(x) is continuous in…

Q: 7. Where is f(x.y)= continuous? Do not just write an answer, show your work or give any necessary…

A:

Q: Which of the following functions are continuous? Why do you think they are continuous? hix fix

A:

Q: Is the following function continuous at a = 1? Explain why. x2 +4x 21 - f(x) = ifx # 3 X - 3 6. ifx…

A: Consider the function  fx=x2+4x−21x−3              x≠36                                 x=3

Q: 3. Which of the following functions is continuous?

A:

Q: Which of the following does not represent a function that is continuous everywhere?

A:

Q: _18. Determine the following function if continuous at f(x) = ) `x + 1' ; at x = 0

A: