Since April 2026
Instructor since April 2026
Translated by Google
Limits in functions using analysis and numerical methods
From 27.92 € /h
Let's take a very simple step-by-step explanation of the Limits lesson 👇
---
🔹 What does Limit mean?
The limit is the value that the function approaches when it gets close to a certain number.
It means we don't have to reach the same point... the important thing is to "get closer to it".
---
🔹 A simple example
If you have:
f(x) = x^2
And we want to calculate:
\lim_{x \to 2} x^2
We try values close to 2:
f(x)=x2
1.9 3.61
1.99 3.9601
2.01 4.0401
👉 For every approximately 2, the result is approximately 4
✔ Therefore:
lim_{x \to 2} x^2 = 4
---
🔹 Basic rule
If the function is continuous, then: 👉 we put the value directly
\lim_{x \to a} f(x) = f(a)
---
🔹 Example with a problem (0/0)
\lim_{x \to 2} \frac{x^2 - 4}{x - 2}
If we compensated:
\frac{4 - 4}{2 - 2} = \frac{0}{0} ❌
This is called an indeterminate form.
---
🔹 How do we solve it?
We analyze:
x^2 - 4 = (x-2)(x+2)
It remains:
\frac{(x-2)(x+2)}{x-2}
In short:
= x + 2
Now let's calculate the final result:
lim_{x \to 2} (x+2) = 4
---
🔹 Types of endings
1. Normal ending
2. End from the right:
\lim_{x \to a^+}
\lim_{x \to a^-}
👉 Both must have the same value for the conclusion to exist.
---
🔹 Important example
f(x) =
\begin{cases}
1 & x < 0 \\
2 & x > 0
\end{cases}
👉 From the north = 1
👉 From right to left = 2
❌ The ending does not exist
---
🔹 Summary
The limit = the value that the function approximates
If there are no problems → compensate directly
If it comes out 0/0 → Disassemble and analyze
Right must equal left
---
If you want: ✔ Solved exercises
✔ Or explain with a diagram
✔ Or a simple video
---
🔹 What does Limit mean?
The limit is the value that the function approaches when it gets close to a certain number.
It means we don't have to reach the same point... the important thing is to "get closer to it".
---
🔹 A simple example
If you have:
f(x) = x^2
And we want to calculate:
\lim_{x \to 2} x^2
We try values close to 2:
f(x)=x2
1.9 3.61
1.99 3.9601
2.01 4.0401
👉 For every approximately 2, the result is approximately 4
✔ Therefore:
lim_{x \to 2} x^2 = 4
---
🔹 Basic rule
If the function is continuous, then: 👉 we put the value directly
\lim_{x \to a} f(x) = f(a)
---
🔹 Example with a problem (0/0)
\lim_{x \to 2} \frac{x^2 - 4}{x - 2}
If we compensated:
\frac{4 - 4}{2 - 2} = \frac{0}{0} ❌
This is called an indeterminate form.
---
🔹 How do we solve it?
We analyze:
x^2 - 4 = (x-2)(x+2)
It remains:
\frac{(x-2)(x+2)}{x-2}
In short:
= x + 2
Now let's calculate the final result:
lim_{x \to 2} (x+2) = 4
---
🔹 Types of endings
1. Normal ending
2. End from the right:
\lim_{x \to a^+}
\lim_{x \to a^-}
👉 Both must have the same value for the conclusion to exist.
---
🔹 Important example
f(x) =
\begin{cases}
1 & x < 0 \\
2 & x > 0
\end{cases}
👉 From the north = 1
👉 From right to left = 2
❌ The ending does not exist
---
🔹 Summary
The limit = the value that the function approximates
If there are no problems → compensate directly
If it comes out 0/0 → Disassemble and analyze
Right must equal left
---
If you want: ✔ Solved exercises
✔ Or explain with a diagram
✔ Or a simple video
Location
Online from Egypt
Age
Teenagers (13-17 years old)
Adults (18-64 years old)
Seniors (65+ years old)
Student level
Advanced
Duration
60 minutes
The class is taught in
Arabic
English
Skills
Availability of a typical week
(GMT -04:00)
New York
Online via webcam
Mon
Tue
Wed
Thu
Fri
Sat
Sun
00-04
04-08
08-12
12-16
16-20
20-24
Similar classes
Contact مدرس رياضيات
1st lesson is backed
by our Good-fit Instructor Guarantee
by our Good-fit Instructor Guarantee
Similar classes
Good-fit Instructor Guarantee
Contact مدرس رياضيات