limit as x approaches 7- of (|x-7|)/(x-7)
1) Compute the limit of as ⁻
ⓘ The limit of a sum of finite limits is the sum of the limits
The limit of is ()⁻ when ⁻
Let's calculate:
ⓘ Start from and move back on the number line, down to zero: =
ⓘ The function abs is continuous, its limit is its value at the limit of its argument
The limit of is ⁺ when ⁻
For , the limit takes the indeterminate form 0/0 when →
2) We need a Taylor expansion for:
Apply the Taylor development of abs with X = around A = (order N =1)
3) We redo the calculation using the Taylor expansion:
The fraction: simplifies by the common factor: into the new expression:
So the limit of is when ⁻
▶Limit:
