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  • Provide solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 3 subquestion (xii)

Provide solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 3 subquestion (xii)

Answers (1)

Answer:

 f(x) is continuous everywhere.

Hint:

 \lim _{x \rightarrow 0} f(x)-g(x)=\lim _{x \rightarrow 0} f(x)-\lim _{x \rightarrow 0} g(x)

Given:

 f(x)=\left\{\begin{array}{cc} \sin x-\cos x & x \neq 0 \\ -1 & x=0 \end{array}\right.

Explanation:

At x = 0

\begin{aligned} &\lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0} \sin x-\cos x \\ &=\lim _{x \rightarrow 0} \sin x-\lim _{x \rightarrow 0} \cos x \\ &=\sin 0-\cos 0 \\ &=-1 \end{aligned}

And

\begin{aligned} &f(x)=-1 \end{aligned}

Constant function,

Sine and cosine function is everywhere continuous and f(x) is continuous at x = 0

\thereforef(x) is everywhere continuous.

Posted by

Gurleen Kaur

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