Calculus is a branch of mathematics that studies continuous change and motion. It is used to model and analyze various real-world phenomena, such as motion, growth, and optimization.
Limits in calculus refer to the value that a function approaches as the input approaches a certain value. It is an essential concept in calculus as it allows us to determine the behavior of a function near a specific point.
To solve calculus problems involving limits, you need to first identify the type of limit (one-sided, two-sided, infinite, etc.). Then, use algebraic manipulation, substitution, or theorems such as L'Hôpital's rule to evaluate the limit.
Integrals in calculus are used to determine the area under a curve or the accumulation of a quantity over a given interval. It is the inverse operation of differentiation and plays a significant role in calculating volumes, areas, and other physical quantities.
To find the area under a curve using integrals, you need to first identify the limits of integration (lower and upper bounds). Then, integrate the function with respect to the independent variable within those limits. The result will be the area under the curve between those limits.