In The given question, , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If a function is differentiable at a point, then it is continuous at that point ?

Q: For which value of a is this function continuous? Please use exact values. { ах — 1 x > 3 f(x) = x2…

A: NOTE: Refresh your page if you can't see any equations. . here the function is continuous so we can…

Q: Will a function that is differentiable on a given interval always be continuous on that interval?…

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Q: f (x) = 2x² – x + 6

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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: 4 x if x 2 3 = x - 2 if 0 < x < 3 x-1 if x <0 %3D

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Q: Determine the domain of the function and prove that it is continuous on its domain using the Laws…

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Q: Is the given statement true or false? Justify your answer. 'If the function f is continuous at a,…

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

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Q: Is the following statement correct? If the function is continuous on R then the constants a and b…

A: It is not necessarily correct that every continuous function on R take the value 2&amp; -2…

Q: Let f(x) = {4x-5, if x &lt;= 7                      -3x + b, if x &gt; 7 If ?(?)f(x) is a function…

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Q: Determine the points where the given function is not defined and is therefore not continuous. For…

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Q: Decide if the following function is continuous using limits. 2x,x0

A: We use left hand limit, right hand limit and function value at 0.

Q: Will a function that is differentiable on a given interval always be continuous on that interval?…

A: Given the statement that " Will a function that is differentiable on a given interval always be…

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

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Q: Find number k, so that f is continuous at every point. 3x+9, if x-6

A: Given,  fx = 3x+9   if   x&lt;-6kx+6   if  x ≥ -6  fx is continuous at every point, then we have to…

Q: Determine whether a function is continuous at a given number. If it is discontinuous, identify which…

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Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: Consider the given function: fx=x-1x-1 This can be written as a split function: fx=-1x&lt;11x&gt;1…

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

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

A: The graph of a function is said to be continuous in an interval if there is no break in ite graph at…

Q: 22. If possible, find constants a and b so that the function f that follows is continuous and…

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

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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: Identify the intervals that the following function is continuous: 0, if x< 2 ={-x² + 6x – 9 , if x 2…

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Q: Determine if the given function is continuous on the given point and intervals.                -x2…

A: The given function is  fx=-x2+4 , x&lt;02x2-5x , 0≤x&lt;37-x  ,    x≥3 We have to check the…

Q: { -2x + 3 x 1

A: We have given a piecewise define a function fx which definition change at x=1. The functions…

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

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Q: Let f(x) | x? + 4x – 5 if x > – 6 - If f(x) is a function which is continuous everywhere, then we…

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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: If f' is continuous, use l'Hospital's Rule to show that f(x + h) – f(x – h) – f'(x) lim 2h Explain…

A: Consider the provided information, limh→0fx+h-fx-h2h=f'x Show that left hand side is equal to right…

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

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Q: At what points are the functions continuous?

A: The part of the function -x2 / 2 is always continuous. There is no point of discontinuity here. The…

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

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Q: х? — 4 if x 3

A: Given: fx=x2-4x-2,x&lt;2ax2-bx+3,2≤x&lt;32x-a+b,x≥3 We know that given function will be continuous…

Q: What values must a and b take for f to be continuous everywhere?

A: Given that the function fx=ax1+4x2 ,      x&lt;0b    ,                     x=0tan-1xx ,…

Q: For what value of a is the following function continuous at every x? a x- 2a, x22 f(x) = 40, x<2…

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Q: At what points is the following function continuous? 3 x - 125 x²2²-25 f(x) = 7.5, 4, X#5, x# -5 x =…

A: Given function:- fx=x3-125x2-25x≠5,x≠-57.5x=54x=-5 Condition for continuity at x=a…

Q: Find numbers a and b, or k, so that f is continuous at every point. 54) -2, ={ ax + b, -5 s x s -3…

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Q: f (x) = 2x² – x + 6 -

A: The given function,   f(x)=2x2-x+6

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

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Q: Determine whether each of the given statements is true. Justify your response with an explanation or…

A: To Determine whether the given statement is True or False: If a function is not continuous at a…

Q: О 1,3] O [-3, -1] О (1,3] O [-3, -1)

A: open circle at a point  signifies that the point is not a part of the solution set  closed circle at…

Q: The graph of the function f'(x) of a continuous function f is shown. On what intervals is f concave…

A: It is given that,the graph of the function f'(x) of a continuous function f.  We have to find…

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

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Q: Decide if the following function is continuous using limits. x1. 2х g(x)= 3

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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: Is the given statement true or false? Justify your answer. 'If the function f is continuous at a,…

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

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Q: -x, x±1 f(x) = 0, x= 1

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Q: x3-9x f (x) = c = -3 x² +11x+24

A: Given function is fx=x3-9xx2+11x+24. To determine whether function is continuous at c=-3. Solution:…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: