TS EAMCET · Maths · Continuity and Differentiability
If \(f: R \rightarrow R\) defined by \(f(x)=\left\{\begin{array}{cc}\frac{1+3 x^2-\cos 2 x}{x^2}, & \text { for } x \neq 0 \k & , \text { for } x=0\end{array}\right.\) is continuous at \(x=0\), then \(k\) is equal to
- A 1
- B 5
- C 6
- D 0
Answer & Solution
Correct Answer
(B) 5
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{rr}\frac{1+3 x^2-\cos 2 x}{x^2}, & \text { for } x \neq 0 \\ k, & \text { for } x=0\end{array}\right.\) RHL \(f(0+h)=\lim _{h \rightarrow 0} \frac{1+3(0+h)^2-\cos 2(0+h)}{(0+h)^2}\) \(=\lim _{h \rightarrow 0} \frac{1+3 h^2-\cos 2 h}{h^2}\)…
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