Lim- a
(X+2)^3/2-(a+2)^3/2/x-a
Answers
Answer:
Answer:
Value of limit :
\frac{5}{2}\cdot (a+2)^\frac{3}{2}
2
5
⋅(a+2)
2
3
Step-by-step explanation:
\begin{gathered}\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}\end{gathered}
x→a
lim
x−a
(x+2)
2
5
−(a+2)
2
5
Adding and subtracting 2 in the denominator
⟹
x→a
lim
(x+2)−(a+2)
(x+2)
2
5
−(a+2)
2
5
Using the property :
x→a
lim
x−a
x
n
−a
n
=n⋅a
n−1
We get,
⟹
x→a
lim
2
5
⋅(a+2)
2
5
−1
=
2
5
⋅(a+2)
2
3