Vänstergränsen

Vänstergränsen, which translates to "left limit" in English, is a fundamental concept in calculus. It refers to the value that a function approaches as its input approaches a particular point from the left side. This is often denoted mathematically as lim x→a⁻ f(x) = L. The superscript minus sign indicates that x is approaching the value 'a' from values less than 'a'.

Understanding the left limit is crucial for analyzing the behavior of functions. It is particularly important when dealing with functions that may have a discontinuity at a specific point. For a function to be continuous at a point 'a', the left limit must exist, the right limit must exist, and the function's value at 'a' must be equal to both of these limits. If the left limit and the right limit at a point are not equal, the function has a jump discontinuity at that point. In cases where the function's value tends towards infinity or negative infinity as the input approaches from the left, the limit is said to not exist in the sense of a finite number, but rather as an infinite limit.