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STD 12 - 5. continuity and differentiation — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 5. continuity and differentiation4 Marks
MCQ
If $y = {a_0} + {a_1}x + {a_2}{x^2} + ..... + {a_n}{x^n},$ then ${y_n} = $
  • A
    $n!$
  • B
    $n!{a_n}x$
  • ✓
    $n!{a_n}$
  • D
    None of these
✓

Answer

Correct option: C.
$n!{a_n}$
c
(c) $y = {a_0} + {a_1}x + ...... + {a_n}{x^n}$

${y_1} = {a_1} + 2{a_2}x + ...... + n{a_n}{x^{n - 1}}$

${y_2} = 2{a_2} + 6{a_3}x + ...... + n(n - 1){a_n}{x^{n - 2}}$
......................................
......................................
${y_n} = n!{a_n}$.

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