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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow a} \frac{(x+2)^{\frac{5}{3}}-(a+2)^{\frac{5}{3}}}{x-a}=$
  • ✓
    $\frac{5}{3}(a+2)^{\frac{2}{3}}$
  • B
    $\frac{5}{3}(a+2)^{\frac{5}{3}}$
  • C
    $\frac{5}{3} a^{\frac{2}{3}}$
  • D
    $\frac{5}{3} a^{\frac{5}{3}}$
✓

Answer

Correct option: A.
$\frac{5}{3}(a+2)^{\frac{2}{3}}$
(A)
$\lim _{x \rightarrow a } \frac{(x+2)^{\frac{5}{3}}-( a +2)^{\frac{5}{3}}}{x- a }=\lim _{x \rightarrow a } \frac{(x+2)^{\frac{5}{3}}-( a +2)^{\frac{5}{3}}}{(x+2)-( a +2)}$
$=\frac{5}{3}(a+2)^{\frac{2}{3}}$

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