15.2. Left-hand Limit
The left-hand limit is the value L as x approaches a number c from the left. It is denoted with a "-" superscript on c. It can be found by plugging in values of x that are less than but close to c.
Consider the function f (x) = x^2 + 2x + 1. Suppose we want to know the limit of f(x) as x approaches 1 from the left. In order to find this limit, you would plug in values that approach 1 but are less than 1. As x gets closer to 1 at 0.99999, y becomes closer to 4.
x 0.9 0.99 0.999 0.9999 0.99999
y 3.61 3.9601 3.996001 3.99960001 3.9999600001 ≈ 4
x 0.9 0.99 0.999 0.9999 0.99999
y 3.61 3.9601 3.996001 3.99960001 3.9999600001 ≈ 4
The graph shows the same approach. As x gets closer to 1 from the left, y gets closer to 4.
So, the left-hand limit of the function is 4.
So, the left-hand limit of the function is 4.
To find the left-hand limit:
1) Type "lim" using the qwerty keyboard.
2) Enter the value being approached using the format: [ x = c -] where c is any real number. Make sure to include the brackets.
3) Enter the function in parentheses if it is longer than one term.
1) Type "lim" using the qwerty keyboard.
2) Enter the value being approached using the format: [ x = c -] where c is any real number. Make sure to include the brackets.
3) Enter the function in parentheses if it is longer than one term.
Three Ways to Find a Limit
1) Type in the word "lim" using the qwerty keyboard. Enable it by tapping the a-z button.
2) Tap the exponent key four times.
3) Tap and hold the exponent key and select "lim."
Examples
Evaluate each left-hand limit.
1) Type in the word "lim" using the qwerty keyboard. Enable it by tapping the a-z button.
2) Tap the exponent key four times.
3) Tap and hold the exponent key and select "lim."
Examples
Evaluate each left-hand limit.
Calculator solution
Type in: lim [ x = π/2 - ] tan (x)
Type in: lim [ x = π/2 - ] tan (x)
Calculator solution
Type in: lim [ x = 4 - ] ( 3 / ( 4 - x )^2 )
Type in: lim [ x = 4 - ] ( 3 / ( 4 - x )^2 )
Calculator solution
Type in: lim [ x = - 2 - ] ( - 4 / ( x + 2 ) )
Type in: lim [ x = - 2 - ] ( - 4 / ( x + 2 ) )
Calculator solution
Type in: lim [ x = 0 - ] ( 6 / x^2 )
Type in: lim [ x = 0 - ] ( 6 / x^2 )
Calculator solution
Type in: lim [ x = 0 - ] ( 1 / x )
Type in: lim [ x = 0 - ] ( 1 / x )
Calculator solution
Type in: lim [ x = 2 - ] ( ( x^2 + 4x - 12 ) / ( x^2 - 2x ) )
Type in: lim [ x = 2 - ] ( ( x^2 + 4x - 12 ) / ( x^2 - 2x ) )