Q&A - Ask Doubts and Get Answers
Q

Show that the function defined by f (x) is equal to cos (x raised to 2) is a continuous function.

31. Show that the function defined byf (x) = \cos (x^2 ) is a continuous function.

Answers (1)
Views

Given function is
f (x) = \cos (x^2 )
given function is defined for all real values of x
Let x = k + h
if x\rightarrow k , \ then \ h \rightarrow 0
f(k) = \cos k^2\\ \lim_{x \rightarrow k}f(x) = \lim_{x \rightarrow k}\cos x^2 = \lim_{h \rightarrow 0}\cos (k+h)^2 = \cos k^2\\ \lim_{x \rightarrow k}f(x) = f(k)
Hence, the function  f (x) = \cos (x^2 ) is a continuous function

Exams
Articles
Questions