Limit
Syntax
lim(Expression, Variable, Value)lim(Expression, Variable, Value, Direction)Examples
Limits
Limits can be calculated using the math template. If + or - is entered in the direction field, it is interpreted as a one-sided limit.
Derivative using the limit definition
The derivative can be defined as the limit of the difference quotient. First the difference quotient is formed, and then its limit is evaluated.
Using CAS, the difference quotient can be calculated symbolically and the limit taken with . The result equals the derivative, which can also be verified directly using 
.
Exploring limits with a slider
Explore limits dynamically by changing the variable's value with a slider. To get more precise results near the critical point, set a small step size for the slider. You can modify the step size and other settings by right-clicking the slider and selecting 'Settings'.
Integral as a sum
An approximate value of an integral can be calculated using a sum by dividing the interval into subintervals. The number of subintervals can be adjusted with a slider, improving the accuracy of the sum. As the number of subintervals increases without bound, the limit of the sum equals the exact value of the integral.