Question

Discuss the continuity of the following functions :
(a) f(x) = sin x + cos x

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Solution

f(x) = sin x + cos x
D_f = R
Let a be any real number.

Lt with straight x rightwards arrow straight a below straight f left parenthesis straight x right parenthesis equals Lt with straight x rightwards arrow straight a below left parenthesis sin space straight x plus cos space straight x right parenthesis plus sin space straight a plus cos space straight a Also space straight f left parenthesis straight a right parenthesis equals sin space straight a plus cos space straight a therefore space straight f left parenthesis straight a right parenthesis equals sin space straight a plus cos space straight a therefore Lt with straight x rightwards arrow straight a below straight f left parenthesis straight x right parenthesis equals straight f left parenthesis straight a right parenthesis therefore space straight f space space is space continuous space at space straight x space equals space straight a But space straight a space is space any space point space of space straight R. space space therefore space straight f space is space continuous space function.

For Daily Free Study Material Join wiredfaculty