Question

What is the difference between Precalculus and Calculus?

Answer 1

Hint: Here we will understand the term Pre-calculus and calculus one by one. Further we will check the topics that are taught in the Pre-calculus segment of mathematics which are then used in the study of calculus. We will classify the topics like relations and functions, limits, derivatives and antiderivatives, trigonometry, logarithms and exponents etc.

Complete step-by-step solution:
Here we have been asked to point out the differences between Precalculus and calculus. First we need to understand these terms related to mathematics.
(1) Pre-calculus: - In mathematics, the term Pre-calculus denotes those topics of mathematics which are studied as building blocks for the topics of calculus. Chapters related to Pre-calculus include algebra, trigonometry, relations and functions, logarithms and exponents, Matrices, polynomial and rational functions, analytical geometry etc. The identities, formulas and certain important concepts of these topics forms the base of calculus.
(2) Calculus: - In mathematics, calculus is the study of continuous change. It has two major parts namely: differential calculus and integral calculus. Differential calculus is the study of instantaneous rate of change in the value of functions, slopes of functions while integral calculus while is the study of accumulation of quantities, area between the curves. Calculus starts with the study of limits which can also be studied in pre-calculus. Other topics of calculus includes: - application of derivatives, continuity and differentiability, area under curves, differentiation, integration etc.

Note: Note that differentiation is the inverse process of integration. Integration of a function of x is given as $\int{f\left( x \right)dx}$ while differentiation of a function of x is given as $\dfrac{d\left( f\left( x \right) \right)}{dx}$. In the topic continuity and differentiability we study if a function is continuous and differentiable at a particular point or not. The concept of limit is used in continuity and differentiability.