Evaluate the following limits :
`Lim_( x to 1 ) [(x-1)^(2) +5] `

Answer

To evaluate the limit \( \lim_{x \to 1} [(x-1)^2 + 5] \), we can follow these steps:

### Step 1: Substitute the limit value into the expression
We start by substituting \( x = 1 \) directly into the expression \( (x-1)^2 + 5 \).

\[ \lim_{x \to 1} [(x-1)^2 + 5] = (1-1)^2 + 5 \]

### Step 2: Simplify the expression
Now, we simplify the expression:

\[ (1-1)^2 + 5 = 0^2 + 5 = 0 + 5 = 5 \]

### Conclusion
Thus, the limit is:

\[ \lim_{x \to 1} [(x-1)^2 + 5] = 5 \]