Mathematics: Single Variable Function Substitution

Based on observations on the activity, it can be concluded that limits of functions do not play a role in calculus.

As you substitute each value of x on the given function, the values of f(x) remain constant.

When comparing the values of f(x) on the right side to the values of f(x) on the left side, they are always equal.

Calculus is also known as Differential Calculus.

The limit laws are not applicable when evaluating the limits of algebraic functions.

In Calculus, the limit process quantifies the relationship between three variables or quantities.

The study of the rate of change is not associated with Calculus.

The existence of a limit of a function as x approaches c depends only on whether f(c) is defined.

If a function is defined at every number in an open interval containing c, then the limit of f(x) as x approaches c is necessarily equal to f(c).

The limit of a function refers to the value that the function approaches at a specific value.

In Calculus, the limit laws apply to polynomial, Rational, and radical functions.

The Constant Rule and Identity Rule are examples of Limit Laws in Calculus.

The sum rule states that if c and k are real numbers, then the limit of c + k as x approaches a exists.

The difference rule states that the limit of f(x) - g(x) as x approaches a is equal to the limit of f(x) as x approaches a minus the limit of g(x) as x approaches a.

According to the product rule in limit laws, the limit of f(x) * g(x) as x approaches a is equal to the limit of f(x) as x approaches a multiplied by the limit of g(x) as x approaches a.

The power rule states that the limit of an expression raised to a positive integer n as x approaches a is equal to the limit of the expression raised to n as x approaches a.

The root rule allows us to find the limit of a function when the variable is inside a root expression.

Indeterminate form may occur when both numerator and denominator of a rational function are zero after direct substitution in a limit evaluation.