How do you find the limit of # (1)/(x-2)# as x approaches #2^+#?

Question

HIX Tutor · Accepted Answer

undefined To find the limit of (1)/(x-2) as x approaches 2^+, you can follow these steps:

1. Substitute the value that x is approaching, which is 2^+ (a number slightly greater than 2), into the expression (1)/(x-2).

2. Simplify the expression by performing the calculation. In this case, (1)/(x-2) becomes (1)/(2^+-2), which is the same as (1)/(small positive number).

3. Remember that when you divide 1 by any small positive number, the result becomes very large. In this case, the result would be infinity.

Therefore, the limit of (1)/(x-2) as x approaches 2^+ is infinity.

Emily Ammerman · Answer

#lim_(xrarr2^+)1/(x-2)=infty# Given, #lim_(xrarr2^+)1/(x-2)# Substitute #x=2^+#. #=lim_(xrarr2^+)1/((2^+)-2# #=lim_(xrarr2^+)1/0^+# #=infty#

Isabella Ackerman · Answer

undefined To find the limit of (1)/(x-2) as x approaches 2^+, we substitute the value of x into the expression. When x approaches 2 from the right side, the denominator (x-2) approaches 0, while the numerator remains constant at 1. Therefore, the limit is positive infinity.