Question

Lim- a

(X+2)^3/2-(a+2)^3/2/x-a

Answer 1

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