15.1. Right-hand Limit of a Function
The right-hand limit is the value L as x approaches a number c from the right. It is denoted with a "+" superscript on c. It can be found by plugging in values of x that are greater 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 right. In order to find this limit, you would plug in values that approach 1 but are greater than 1. As x gets closer to 1 at 1.000001, y becomes closer to 4.
x 1.1 1.01 1.001 1.0001 1.00001 1.000001
y 4.41 4.0401 4.004 4.0004 4.00004 4.000004 ≈ 4
x 1.1 1.01 1.001 1.0001 1.00001 1.000001
y 4.41 4.0401 4.004 4.0004 4.00004 4.000004 ≈ 4
The graph above shows the same approach. As x approaches 1, y gets closer to 4.
So, the right-hand limit of the function is 4.
So, the right-hand limit of the function is 4.
Calculator Syntax: lim[x = 1+](x^2 + 2x + 1)
Three Ways to Enter a Limit
1) Type in the word "lim" using the qwerty keyboard. Access it by tapping the a-z button.
1) Type in the word "lim" using the qwerty keyboard. Access it by tapping the a-z button.
2) Use the limit function by tapping the exponent key four times.
3) Tap and hold the exponent key. Then select "lim."
Finding the right-hand limit
1) Type "lim" using the qwerty keyboard.
2) Enter the value c being approached by using the format: [ x = c + ] , where c is any real number. Make sure to include the brackets.
3) Enter the function. Use parentheses if it is longer than one term such as a rational function.
1) Type "lim" using the qwerty keyboard.
2) Enter the value c being approached by using the format: [ x = c + ] , where c is any real number. Make sure to include the brackets.
3) Enter the function. Use parentheses if it is longer than one term such as a rational function.
Examples
Evaluate each right-hand limit.
Evaluate each right-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 = 0 + ] ln (x)
Type in: lim [ x = 0 + ] ln (x)
Calculator solution
Type in: lim [ x = 4 + ] ( 3 / (4 - x) ^3)
Type in: lim [ x = 4 + ] ( 3 / (4 - x) ^3)
Calculator solution
Type in: lim [ x = - 2 + ] ( -4 / (x+2) )
Type in: lim [ x = - 2 + ] ( -4 / (x+2) )
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 ) )
Calculator solution
Type in: lim [ z = 1 + ] ( ( 6 - 3z + 10z^2 ) / ( -2z^4 + 7z^3 +1 ) )
Type in: lim [ z = 1 + ] ( ( 6 - 3z + 10z^2 ) / ( -2z^4 + 7z^3 +1 ) )