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99 Percentile Qs Bank for JEE MainMathematicsLimits

lim n → ∞ P 1 + r 100 n t n =

Options

  1. AP
  2. BP 1 + r 100 t
  3. CP e r t 100
  4. DP e r 100

Correct answer

C. P e r t 100

Step-by-step solution

Let, y = lim n → ∞ P 1 + r 100 n t n Let, n = 1 x so when n → ∞ then x → 0 . ∴ y =   lim x → 0 P 1 + r x 100 t x Taking log on both sides, we get ln y =   lim x → 0   ln P 1 + r x 100 t x ⇒ ln y =   lim x → 0   ln P + t x ln 1 + r x 100 ⇒ ln y = ln P + lim x → 0   t ln 1 + r x 100 r x 100 × r 100 ⇒ ln y - ln P = r t 100 ∵ lim x → 0 ln 1 + x x = 1 ⇒ ln y P = r t 100 ⇒ y P = e r t 1

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