戰昇的部落格

(1 point)

Why is the following function discontinuous at x=0�=0?

(a) f(0)�(0) does not exist.
(b) limx→0f(x)lim�→0�(�) does not exist (or is infinite).
(c) Both (a) and (b).
(d) f(0)�(0) and limx→0f(x)lim�→0�(�) exist, but they are not equal.

(1 point)

Which of the following is a function that has a jump discontinuity at x=2�=2 and a removable discontinuity at x=4�=4, but is continuous elsewhere?

(a) f(x)=2(x−2)(x−4)�(�)=2(�−2)(�−4).

(b) f(x)=⎧⎩⎨1x−33if x≤2if 2<x<4 or x>4if x=4�(�)={1if �≤2�−3if 2<�<4 or �>43if �=4.

(c) f(x)=⎧⎩⎨2−x21x2−4xif x≤2if x>2�(�)={2−�2if �≤21�2−4�if �>2.

(1 point)

If f(x)=x3−x2+x�(�)=�3−�2+�, is there a number c� such that f(c)=10�(�)=10?
Answer "y" for yes or "n" for no below.

(1 point) Find the value of the constant c� that makes the following function continuous on (−∞,∞)(−∞,∞).

c=�= 

(1 point)

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�(�)=�2−2�−8�+2, a=−2�=−2

(b) f(x)=x−7|x−7|�(�)=�−7|�−7|, a=7�=7

(c) f(x)=x3+64x+4�(�)=�3+64�+4, a=−4�=−4

(d) f(x)=3−x√9−x�(�)=3−�9−�, a=9�=9

(a) 
(b) 
(c) 
(d)