2x - 5x – 3 7. f(x) = if x # 3 x- 3 ,a = 3 6 if x = 3

Q: f(x) : ²+4x-5 a+5 c = - 5

A: The objective of the question is checking the continuity of the given function at given point.

Q: Use the definition of continuity to determine whether f is continuous at a. f(x) =(x2 + 6)/(x - 5) a…

A: A function f(x) is said to be continuous at a point x = a, if 1) f(a) exists. 2) limx→af(x)exists.…

Q: Use the definition of continuity to determine whether f is continuous at a. f(x) = 3x2 - 2x + 1 a =…

A: Given, fx=3x2-2x+1 To determine whether the function f(x) is continuous at x=4

Q: Test the continuity of the following functions at given points? r2

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: Determine if the following function is continuous or discontinuous at x = 0? 4 +5 f(z) = 9-3z

A:

Q: Use the definition of continuity to determine whether f is continuous at a. f(x) =(x2 + 4)/(x - 2) a…

A: Given the function f(x)=(x2 + 4)/(x - 2) We need to use the definition of continuity to determine…

Q: 3. J Use the definition of continuity and the properties of limits to show that the function is…

A: As per bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Use the definition of continuity to determine whether f(x) = 2x + 5 at a = 1.

A: Given function is fx=2x+5.

Q: Use the definition of continuity to determine whether the shown is continuous at a = 2.

A:

Q: if x<0 ifx = 0 黑,ir0 <xく3 x+6, ifx23 13,

A:

Q: Use the definition of continuity to determine whether f is continuous at a. f(x) =(x + 7)/(x - 7) a…

A: Given, f(x)= x+7x-7 and point a= 7 To determine: f is continuous at a Definition of continuity :  A…

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: Determine whether the following function is continuous at a. Use the continuity checklist to justify…

A: We have to check

Q: Use the definition of continuity and the properties oflimits to show that the function is continuous…

A:

Q: Use the definition of continuity to decide if the following function is continuous at a = -1. -1.0x²…

A:

Q: Analyze the continuity of the following function f(x) = 4x + 10      0 ≤ x ≤ 15 at the point x=8

A: The answer is given below:

Q: Use the definition of continuity to determine whether f is continuous at a. f(x) =(x - 5)/(x + 5) a…

A: If the function is continuous at x=a then it must satisfy the conditions of continuity.  The value…

Q: Determine whether the following functions are continuous at a. Use the continuity checklist to…

A: Given, f(x)=x2-4x+3x-3   ifx≠32                  ifx=3;a=3 find the continuity of function at x=3 if…

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

A:

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: Determine whether the following functions are continuous at a. Use the continuity checklist to…

A: Given: fx=2x2+3x+1x2+5x,a=-5

Q: (x – 2)2 +1 if x 2

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

Q: f(x) = x² + /7 – x, a=4

A: We have sove limit and showing function

Q: f(x) = x² + /7 – x, a = 4

A: A function is said to be continuous on the interval [a, b] if it is continuous at each point in that…

Q: Use the definition of continuity and the properties of limits to show that the function is…

A: We have to use the definition of continuity and the properties of limits to show that the function…

Q: Suppose fx) is defined as shown below. a. Use the continuty checklist to show that f is not…

A: we have to check the functions continuous at x=1 Yes or not  Using left hand limit and right hand…

Q: f (x) 1 ; x = - 5 %3D | x+5

A:

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A: f(x) = x4 − 81x is a polynomial function.

Q: fx +1 1 if x = 1 5. f(x) = ,a = 1

A:

Q: Determine whether the statement is true or false. If f is continuous at 5 and f(5) = 3 and f(4) = 3,…

A:

Q: (c) Consider the following graph of a function y = f(x): -2 -1 3 Test the continuity of f(x) at x =…

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Q: Determine the interval(s) on which the following function is continuous. At which finite endpoints…

A: Given function is

Q: Consider the function defined by f(x) = -(x + 1)² +5 if x 4 Graph the function. Is the function…

A:

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A:

Q: Explain why the function is discontinuous at 4 using definition of continuity. What type of…

A: Given f(x)=x2-x-12x-4 Explain why the function is discontinuous at 4 using definition of continuity.…

Q: 6et-8) _6 if 0 8

A:

Q: b) Discuss the continuity conditions of the function- f(x) which shown in figure at x= 0,x = 1,x= 2…

A:

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

A:

Q: Determine whether the following function is continuous at a. Use the continuity checklist to justify…

A:

Q: Classify the statement as either true or false. If f is continuous at x= 2, then f(2) must exist,…

A: Given query is to find statement is true or false.

Q: a) f(x) at x = 0 b) fx) 3x at x = -4 X-7

A: a) f(x)=6x at x=0b) f(x)=3xx-7 at x=-4

Q: Identify the removable discontinuity and define the continuous extension of the function. x² + 7x –…

A:

Q: Determine whether the following function is continuous at the given point z= 22 +9z – 5 f(=) = 2x-1…

A:

Q: Determine the set of points at which the function is continuous

A: Given function

Q: Determine whether the following function is continuous at the given point z = 3x2 + 17z - 6 f(x) =…

A: A function f(x) is said continous at x = a  only when

Q: Consider the following figure. y f(x) whether the function is continuous or discontinuous at that…

A: Given query is to check the characteristics of function for x = -2.

Q: Is the following function continuous at r= 5? Explain your answer. 5x if r 5

A: Given  f(x) = 5xif x&lt;512if x=5x2if x&gt;5 We have to check the continuity at x=5.

Q: Determine if each function is continuous at the given value of a. Justify your answers using limits…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

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.