How do limits work in calculus?

Question

Aurora Alvarado · Accepted Answer

In Pre-Calculus, they function similarly. Limits convey the action of approaching a coordinate in a graph that may or may not exist in the curve itself, whether it's due to an asymptote or a discontinuity. It tends to describe a value that you are unsure exists and can be used as a systematic way of determining whether or not it does. You can approach from the left or right in a #y = f(x)# graph. For example:
#lim_(x->0^+) 1/x = oo#
"The limit as x approaches 0 from the positive/right side of #1/x# is infinity" #lim_(x->0^-) 1/x = -oo#
"The limit as x approaches 0 from the negative/left side of #1/x# is negative infinity" #lim_(h->0) [f(x+h) - f(x)]/h#
"The limit as #h# approaches a very small number from either side of #(f(x+h) - f(x))/h# is the slope of the function #h# units away from the point of examination" which basically says that if you zoom in very far into a function, it looks linear and you can use the basic slope formula at that close zoom to find the slope. #h# is some very small value, hence the #h->0#.

Axel Alvarez · Answer

undefined Limits in calculus are used to describe the behavior of a function as it approaches a certain value or as it approaches infinity. They are fundamental in understanding concepts such as continuity, derivatives, and integrals. A limit is defined as the value that a function approaches as the input approaches a particular value. It can be approached from both the left and right sides. Limits can be evaluated algebraically, graphically, or using various limit laws and theorems. They allow us to analyze the behavior of functions and make precise calculations in calculus.