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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Limits

NDA 2023 · Mathematics · Limits

Let f(x)=|x| and g(x)=[x]-1 , where [.] is the greatest integer...

Let f(x)=∣x∣f(x)=|x| and g(x)=[x]−1g(x)=[x]-1, where [.] is the greatest integer function. Let h(x)=f(g(x))g(f(x))h(x)=\frac{f(g(x))}{g(f(x))}. What is lim⁡x→0+h(x)\lim _{x \rightarrow 0+} h(x) equal to?

Options

  1. A-2
  2. B-1
  3. C0
  4. D1

Correct answer

B. -1

Step-by-step solution

Since, h(x)=f(g(x))g(f(x))=f([x]−1)g(∣x∣)=∣[x]−1∣[∣x∣]−1h(x)=\frac{f(g(x))}{g(f(x))}=\frac{\mathrm{f}([\mathrm{x}]-1)}{\mathrm{g}(|\mathrm{x}|)}=\frac{|[\mathrm{x}]-1|}{[|\mathrm{x}|]-1} Since,=lim⁡x→0+∣[x]−1∣[x]−1=∣−1∣−1=−1=\lim _{x \rightarrow 0^{+}} \frac{|[\mathrm{x}]-1|}{[x]-1}=\frac{|-1|}{-1}=-1
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