To solve the limit:

\[
\lim_{x \to 2} (x^3 + x^2 + 5)
\]

we can directly substitute \( x = 2 \) into the expression since it is a polynomial and continuous at \( x = 2 \).

\[
= (2^3 + 2^2 + 5)
\]

First, calculate each part:

\[
2^3 = 8, \quad 2^2 = 4
\]

Now sum them up:

\[
8 + 4 + 5 = 17
\]

Thus, the limit is:

\[
\lim_{x \to 2} (x^3 + x^2 + 5) = 17
\]

Do you have any questions or would you like further details?

Here are 5 related questions:
1. What is the limit of \( \lim_{x \to 3} (x^3 + x^2 + 5) \)?
2. How would you find the limit if the function was not continuous?
3. What happens to the limit if the polynomial included a negative term?
4. Can limits exist for non-polynomial functions at given points?
5. How can we use L'Hopital's Rule for more complex limits?

**Tip:** For continuous functions like polynomials, the limit can be found simply by direct substitution of the value.

Discover how to calculate the limit of the polynomial function lim_{x→2} (x^3 + x^2 + 5) by using direct substitution. This step-by-step guide explains the concept of limits and continuity. Ideal for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation