https://file.aiquickdraw.com/mathbot/file/1725545421803u3oxlrsn.jpg

The limit given in the image is:

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

To solve this limit, we can directly substitute \(x = -3\) into the expression, as this is a polynomial and does not have any discontinuities or indeterminate forms.

1. First, substitute \(x = -3\) into the expression \(x^2 + 3x\):
\[
(-3)^2 + 3(-3) = 9 - 9 = 0
\]

Thus, the limit is:
\[
\lim_{{x \to -3}} (x^2 + 3x) = 0
\]

Would you like a deeper explanation on the steps, or do you have any additional questions? 

Here are five related questions you might find useful:
1. What is the definition of a limit in calculus?
2. How do you find limits involving indeterminate forms?
3. Can limits be solved graphically? If so, how?
4. What is the difference between one-sided and two-sided limits?
5. What are some common types of functions where limits cannot be found directly?

**Tip:** When dealing with polynomial functions, you can often find limits by direct substitution, as these functions are continuous everywhere!

Find the limit of the following: lim(x^2 + 3x) as x → -3

This page explains how to find the limit of the polynomial expression x^2 + 3x as x approaches -3. Using the direct substitution method, this example shows that the limit is 0. Perfect for students in Grades 10-12 looking to understand limits of polynomials.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation