III. 2. Consider the function x<0 0SAS1 (1) At what points is this function continues? (2) For each point a, where the function is not continuous, compute lim, f(x), lim, f(x)

Q: Consider the piecewise defined function Find the values of a and b that make the following function…

A:

Q: Carefully sketch the graph of a continuous function f which satisfies the following properties:

A: Given, Sign of f'x-f'x&lt;0 on an interval -∞,-2. f'x&gt;0 on an interval -2,0. f'x&lt;0 on an…

Q: Let f(z) 2 = = (-)². Show that lim f(z) does not exist. z➡0

A:

Q: 6. Is it true that the limit of a function lim f(c) = L is the same as evaluating a function f(c)?

A: the limit of a function lim f(c) = L is the same as evaluating a function f(c)

Q: Find the domain of the function f(x) = /2x – 3 - In interval form, the domain of f is

A: here function is given in form of square root this can't be negative so the value inside is positive…

Q: n each part below, give an example of a function which satisfies the given criteria. Justify that…

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Q: The function f is continuous for all real numbers. If lim f(x) = 0, then what is lim xe-2x)? x-2 x-1

A: The function f is continuous for all real numbers  If limx→2f(x)=0then if we put x=2t then…

Q: 3. If f is a continuous function, what can you say about lim f(x)?

A: Given thatf is continuous To determinelimx→1f(x)

Q: (c) Find the constants a and b so that the function f (x) is continuous everywhere. Also graph the…

A: Solution:Given  f(x)=x+aif -∞&lt;x&lt;4(x-1)2if 4≤x≤9Bx+1if 9&lt;x&lt;∞To find 'a' and 'b'Also graph…

Q: 7. (a) List the condition(s) for a function to f(x) be continuous at the point x = c. (b) For the…

A: 7. The given function gx=2x+a+x+3x+2x&gt;-2x+4+bx≤-2. We have to find the values of a and b, such…

Q: Consider the following. X = if x 1 Find the left-hand and right-hand limits. lim f(z) f(x). lim f…

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Q: Sketch a graph of a function that satisfies all of the following properties. -4- a) f(-6) is…

A: We need to sketch the graph.