COMEDK · Maths · 16. Limits
The value of \(\quad \lim _{x \rightarrow 0} \dfrac{(1-x)^n-1}{x}=\)
- A \(0\)
- B \(1\)
- C \(n\)
- D \(-n\)
Answer & Solution
Correct Answer
(D) \(-n\)
Step-by-step Solution
Detailed explanation
Let \(f(x) = (1-x)^n\). The given limit is of the form \(\lim_{x \to 0} \dfrac{f(x) - f(0)}{x - 0}\), which is the definition of the derivative \(f'(0)\). Calculate the derivative of \(f(x) = (1-x)^n\) with respect to \(x\):…
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