Evaluate the following limits :
`Lim_(x to 0 ) (7x^(2) - 5x +1)`

Answer

To evaluate the limit \( \lim_{x \to 0} (7x^2 - 5x + 1) \), we can follow these steps:

### Step 1: Identify the limit expression
We are given the expression \( 7x^2 - 5x + 1 \) and we need to evaluate the limit as \( x \) approaches 0.

### Step 2: Check the form of the limit
Since substituting \( x = 0 \) does not lead to an indeterminate form (like \( \frac{0}{0} \)), we can directly substitute the value of \( x \).

### Step 3: Substitute \( x = 0 \)
Now, we substitute \( x = 0 \) into the expression:
\[ 7(0)^2 - 5(0) + 1 \]

### Step 4: Simplify the expression
Calculating this gives:
\[ 7 \cdot 0 - 5 \cdot 0 + 1 = 0 - 0 + 1 = 1 \]

### Step 5: State the limit
Thus, we find that:
\[ \lim_{x \to 0} (7x^2 - 5x + 1) = 1 \]

### Final Answer
The limit is \( 1 \).

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