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JEE Main 2003
Exam
JEE Main
Year
2003
Subject
Mathematics
Chapter
Limits

JEE Main 2003 · Mathematics · Limits

Let f(a)=g(a)=k and their n th derivatives f^ n (a), g^ n (a) exist...

Let f(a)=g(a)=k\mathrm{f}(\mathrm{a})=\mathrm{g}(\mathrm{a})=\mathrm{k} and their nnth derivatives fn(a),gn(a)\mathrm{f}^{\mathrm{n}}(\mathrm{a}), \mathrm{g}^{\mathrm{n}}(\mathrm{a}) exist and are not equal for some n\mathrm{n}. Further if lim⁡x→af(a)g(x)−f(a)−g(a)f(x)+f(a)g(x)−f(x)=4\lim _{x \rightarrow a} \frac{f(a) g(x)-f(a)-g(a) f(x)+f(a)}{g(x)-f(x)}=4 then the value of kk is

Options

  1. A0
  2. B4
  3. C2
  4. D1

Correct answer

B. 4

Step-by-step solution

lim⁡x→ak9(x)−kf(x)9(k)−f(x)=4\lim _{x \rightarrow a} \frac{k 9(x)-k f(x)}{9(k)-f(x)}=4 (By L'Hospital rule) lim⁡x→ak9′(x)−f′(x)9′(x)−f′(x)=4\lim _{x \rightarrow a} k \frac{9^{\prime}(x)-f^{\prime}(x)}{9^{\prime}(x)-f^{\prime}(x)}=4 or k=4k=4
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