At - 27 :t< 3 h(t) = cos (t) :t>3 where A is a constant whose value can be chosen. a) What is the value of h(t) when t = 3? (Your answer may or may not depend on A.) b) What is the value of lim h(t)? (Your answer may or may not depend on A.) c) What is the value of lim h(t)? (Your answer may or may not depend on A.) d) Will h(t) be continuous or discontinuous at t = 3 if we use A = 1? If discontinuous, what type of discontinuity will h(t) have at this point? e) What value(s) can be used for A to ensure that h(t) is continuous on its domain?
At - 27 :t< 3 h(t) = cos (t) :t>3 where A is a constant whose value can be chosen. a) What is the value of h(t) when t = 3? (Your answer may or may not depend on A.) b) What is the value of lim h(t)? (Your answer may or may not depend on A.) c) What is the value of lim h(t)? (Your answer may or may not depend on A.) d) Will h(t) be continuous or discontinuous at t = 3 if we use A = 1? If discontinuous, what type of discontinuity will h(t) have at this point? e) What value(s) can be used for A to ensure that h(t) is continuous on its domain?
At - 27 :t< 3 h(t) = cos (t) :t>3 where A is a constant whose value can be chosen. a) What is the value of h(t) when t = 3? (Your answer may or may not depend on A.) b) What is the value of lim h(t)? (Your answer may or may not depend on A.) c) What is the value of lim h(t)? (Your answer may or may not depend on A.) d) Will h(t) be continuous or discontinuous at t = 3 if we use A = 1? If discontinuous, what type of discontinuity will h(t) have at this point? e) What value(s) can be used for A to ensure that h(t) is continuous on its domain?
The piecewise function h(t) is defined by the formula: (please refer to the attached image below) where A is a constant whose value can be chosen.
Transcribed Image Text:At? - 27 :t< 3
h(t) =
cos (t) :t>3
where A is a constant whose value can be chosen.
a) What is the value of h(t) when t = 3? (Your answer may or may not depend on A.)
b) What is the value of lim h(t)? (Your answer may or may not depend on A.)
c) What is the value of lim h(t)? (Your answer may or may not depend on A.)
d) Will h(t) be continuous or discontinuous at t = 3 if we use A = 1? If discontinuous, what type of discontinuity will
h(t) have at this point?
e) What value(s) can be used for A to ensure that h(t) is continuous on its domain?
Definition Definition Group of one or more functions defined at different and non-overlapping domains. The rule of a piecewise function is different for different pieces or portions of the domain.
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