Why is the following function discontinuous at x=0?
(a) f(0) does not exist.
(b) limx→0f(x) does not exist (or is infinite).
(c) Both (a) and (b).
(d) f(0) and limx→0f(x) exist, but they are not equal.
Which of the following is a function that has a jump discontinuity at x=2 and a removable discontinuity at x=4, but is continuous elsewhere?
(a) f(x)=2(x−2)(x−4).
(b) f(x)=⎧⎩⎨1x−33if x≤2if 2<x<4 or x>4if x=4.
(c) f(x)=⎧⎩⎨2−x21x2−4xif x≤2if x>2.
If f(x)=x3−x2+x, is there a number c such that f(c)=10?
Answer "y" for yes or "n" for no below.
Find the value of the constant c that makes the following function continuous on (−∞,∞).
c=
For the functions below that have a removable discontinuity at x=a [if the function does not have a removable discontinuity, type in "n" below], state the value of g(a), where g(x) agrees with f(x) for x≠a and is continuous everywhere.
(a) f(x)=x2−2x−8x+2, a=−2
(b) f(x)=x−7|x−7|, a=7
(c) f(x)=x3+64x+4, a=−4
(d) f(x)=3−x√9−x, a=9
Consider the function f(x)=2x3+2x2+13. For what values of k does the Intermediate Value Theorem tell us that there is a c in the interval [0,1] such that f(c)=k?
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