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  • Explain solution RD Sharma class 12 chapter Continuity exercise 8.2 question 15 maths

Explain solution RD Sharma class 12 chapter Continuity exercise 8.2 question 15 maths

Answers (1)

Answer:

 |cos x| is continuous.

Hint:

 Continuous of two continuous functions is continuous.

Given:

 f(x) = |cos x|

Explanation:

 f(x) = |cos x|

Let a be any real number

L.H.L

\begin{aligned} &\lim _{x \rightarrow a^{-}} f(x)=\lim _{h \rightarrow 0} f(a-h) \\ &=\lim _{h \rightarrow 0}|\cos (a-h)| \\ &=|\cos a| \end{aligned}

R.H.L

\begin{aligned} &\lim _{x \rightarrow a^{+}} f(x)=\lim _{h \rightarrow 0} f(a+h) \\ &=\lim _{h \rightarrow 0}|\cos (a+h)| \\ &=\cos a \end{aligned}

L.H.L = R.H.L = f(a)

f(x)  is continuous everywhere

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Gurleen Kaur

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