_ x 2 x^ 7 2 -2^ 7 2 x^ 3 2 -2^ 3 2 = - Vidyadip

MCQ

$\lim _{x \rightarrow 2} \frac{x^{\frac{7}{2}}-2^{\frac{7}{2}}}{x^{\frac{3}{2}}-2^{\frac{3}{2}}}=$

✓
$\frac{28}{3}$
B
$\frac{34}{3}$
C
$\frac{29}{2}$
D
$\frac{35}{3}$

✓

Answer

Correct option: A.

$\frac{28}{3}$

(A)
$\lim _{x \rightarrow a} \frac{x^m-a^m}{x^n-a^n}=\frac{m}{n} a^{m-n}$
$\lim _{x \rightarrow 2} \frac{x^{\frac{7}{2}}-2^{\frac{7}{2}}}{x^{\frac{3}{2}}-2^{\frac{3}{2}}}=\frac{7}{2} \times \frac{2}{3}(2)^{\frac{7}{2}-\frac{3}{2}}=\frac{7}{3} \times 4=\frac{28}{3}$

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