3. Liskov Substitution Principle (LSP)

Concept: Objects in a program should be replaceable with instances of their subtypes without altering the correctness of the program.

4. Interface Segregation Principle (ISP)

Concept: No client should be forced to depend on methods it does not use.

5. Dependency Inversion Principle (DIP)

Concept: High-level modules should not depend on low-level modules. Both should depend on abstractions. Furthermore, abstractions should not depend on details; details should depend on abstractions.

The SOLID design principles are a set of five guidelines in object-oriented programming that help developers create more maintainable, understandable, and flexible software. Each letter in "SOLID" stands for a principle:

1. Single Responsibility Principle (SRP)

Concept: A class should have one, and only one, reason to change.

2. Open/Closed Principle (OCP)

Concept: Software entities (classes, modules, functions, etc.) should be open for extension, but closed for modification.

L’Hospital’s rule is a way to figure out some limits that you can’t just calculate on their own. Precisely, to estimate the limit of a fraction that, when it gives 0/0 or ∞/∞, we often use L’Hopital’s rule.

How do you prove the L Hospital rule?
Suppose L = lim_{x→a} f(x)/g(x), where both f(x) and g(x) results to ∞ or −∞ as x→a.
Also, when L is neither 0 nor ∞.
Thus, L Hospital rule can be proved as L = lim_{x→a} f(x)/g(x) = lim_{x→a} [1/g(x)]/ [1/f(x)].

L’Hospital’s Rule only applies when the expression is indeterminate, i.e. 0/0 or (+/-infinity)/(+/-infinity). Hence, we have to stop applying the rule when you have a deductive form.

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0/0 or ±∞/±∞.