find the limit of (2x^2-4+5) as x approaches to -3

The expression provided is:

\[
2x^2 - 4 + 5
\]

First, simplify the expression:

\[
2x^2 - 4 + 5 = 2x^2 + 1
\]

Now, find the limit as \( x \) approaches \(-3\):

\[
\lim_{x \to -3} \left( 2x^2 + 1 \right)
\]

Substitute \( x = -3 \) into the expression:

\[
2(-3)^2 + 1 = 2(9) + 1 = 18 + 1 = 19
\]

Therefore, the limit is:

\[
\boxed{19}
\]

Would you like further details or have any questions? 

Here are 5 related questions:

1. What is the limit of \( x^2 - 3x + 2 \) as \( x \) approaches 2?
2. How do you find the limit of a polynomial function as \( x \) approaches a given value?
3. Can the limit of a function be different from the function's value at that point?
4. What happens to the limit if you approach \(-3\) from the right or left side?
5. How would the limit change if the expression had been \(2x^2 - 4x + 5\)?

**Tip:** When finding the limit of a polynomial, directly substitute the value into the polynomial if the function is continuous.

Learn how to find the limit of the polynomial function 2x^2 - 4 + 5 as x approaches -3. This problem involves evaluating a polynomial function and applying the concept of limits in calculus. Suitable for advanced high school students or those studying introductory calculus.

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