Question

SCALCET9 2.5.023. Explain why the function is discontinuous at the given number a. (Select all that apply.) f(x) = { cos(x) if x < 0, 0 if x = 0, 1 - x^2 if x > 0, a = 0 lim x->0 f(x) does not exist. f(0) is undefined. f(0) and lim x->0 f(x) are finite, but are not equal. lim x->0+ f(x) and lim x->0- f(x) are finite, but are not equal. none of the above Sketch the graph of the function.

          SCALCET9 2.5.023.
Explain why the function is discontinuous at the given number a. (Select all that apply.)
f(x) = { cos(x) if x < 0, 0 if x = 0, 1 - x^2 if x > 0, a = 0
lim x->0 f(x) does not exist.
f(0) is undefined.
f(0) and lim x->0 f(x) are finite, but are not equal.
lim x->0+ f(x) and lim x->0- f(x) are finite, but are not equal.
none of the above
Sketch the graph of the function.

SCALCET9 2.5.023.
Explain why the function is discontinuous at the given number a. (Select all that apply.)
f(x) = cos(x) if x < 0, 0 if x = 0, 1 - x^2 if x > 0, a = 0
lim x->0 f(x) does not exist.
f(0) is undefined.
f(0) and lim x->0 f(x) are finite, but are not equal.
lim x->0+ f(x) and lim x->0- f(x) are finite, but are not equal.
none of the above
Sketch the graph of the function.

Added by Maurice P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Gregory Higby

04/07/2023

Step 1

We know that the cosine function is continuous for all real numbers. Now, let's check the continuity of the function at a given number, say $a$. For a function to be continuous at a point $a$, the following conditions must be satisfied: Show more…

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SCALCET9 2.5.023. Explain why the function is discontinuous at the given number a. (Select all that apply.) f(x) = { cos(x) if x < 0, 0 if x = 0, 1 - x^2 if x > 0, a = 0 lim x->0 f(x) does not exist. f(0) is undefined. f(0) and lim x->0 f(x) are finite, but are not equal. lim x->0+ f(x) and lim x->0- f(x) are finite, but are not equal. none of the above Sketch the graph of the function.