The organism reacts to the stimulus and shows a certain reaction when s(t) ≥ 1/2. Define a function g(t) such that g(t) = 0 when the organism shows no reaction at time t and g(t) = 1 when the organism shows the reaction.

(a) Plot s(t) and g(t) in the same coordinate system.

(b) Is s(t) continuous? Is g(t) continuous?
in Calculus Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer


(a) s(t) is shown as the red curve, g(t) is shown as the green lines. The blobs on the ends of a line mean the end points are included, and when there are no blobs, the end points are excluded. The blue line divides s(t) into two parts to show when it’s greater than or when it’s less than a half. You can see from this line how the decision is made to draw the green line along the t axis (g(t)=0) or at g(t)=1.

(b) s(t) is continuous, but g(t) is discontinuous because it jumps between 0 and 1.

g(t)={ 0 | sin(πt)≤½

        { 1 | sin(πt)>½

where t≥0

The switch from 0 to 1 and vice versa occurs at t=⅙, ⅚, 2⅙, 2⅚, 4⅙, 4⅚, etc. So the organism reacts for ⅓ of the time, and fails to react for ⅔ of the time for every cycle.

Another way of defining g(t) is:

g(t)={ 0 | 0≤t≤⅙

        { 1 | 2n+⅙<t<2n+⅚

        { 0 | 2n+⅚≤t≤2(n+1)+⅙

where n is an integer and n≥0

by Top Rated User (616k points)

Related questions

Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
82,260 questions
86,784 answers
3,660 users