Show that f is continuous on (-infty , infty). f(x)={(sin(x) if x<pi/4),(cos(x) if xge pi/4):}

Nelson Jennings

Nelson Jennings

Answered question

2022-07-25

Show that f is continuous on ( , ).
f ( x ) = { sin ( x )   i f   x < π / 4 cos ( x )   i f   x π / 4

Answer & Explanation

Coleman Ali

Coleman Ali

Beginner2022-07-26Added 13 answers

you know that the sine ans cosine functions are continuousbecause all the regions of the graph are defined...the only problemis the transition between the two function at π / 4
so you would have to prove that sin ( π / 4 ) = cos ( π / 4 )
since sin ( π / 4 ) = cos ( π / 4 ) = 2 / 2 = 0.7071
where one functions ends, the other begins, making thetransition seamless and thus, it is a continuous functions.

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