No need to restrict to the right limit. By variable change u = x − 1, this is lim u → 0 1 ln ( 1 + u) − 1 u = lim u → 0 u − ln ( 1 + u) u ln ( 1 + u). 1) L'Hospital: if we differentiate once top and bottom
A right-hand limit means the limit of a function as it approaches from the right-hand side. Step 1: Apply the limit x 2 to the above function. Put the limit value in place of x. lim x → 2 + ( x 2 + 2) (
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To why this is true, remember that x is approaching 1 from the right. This means that will be small and positive. On the other hand, . Since the top is negative and the bottom is positive, the result must be negative . As far as size goes, I have