Question

Lim x tends to a (x+2)^5/2 - (a+2)^5/2 ÷ x-a plzzz solve it by general method

Answer 1

The answer is in the pic ....Hope it helps

Answer 2

Answer:

Value of limit :

$\frac{5}{2}\cdot (a+2)^\frac{3}{2}$

Step-by-step explanation:

$\lim_{x\to a} \frac{(x+2)^{\frac{5}{2}}-(a+2)^{\frac{5}{2}}}{x-a}\\\\\text{Adding and subtracting 2 in the denominator}\\\\ \implies\lim_{x\to a} \frac{(x+2)^{\frac{5}{2}}-(a+2)^{\frac{5}{2}}}{(x+2)-(a+2)}\\\\\text{Using the property : }\lim_{x\to a}\frac{x^n-a^n}{x-a}=n\cdot a^{n-1}\text{ We get, }\\\\\implies \lim_{x\to a }\frac{5}{2}\cdot (a+2)^{\frac{5}{2}-1}\\\\=\frac{5}{2}\cdot (a+2)^\frac{3}{2}$