Question

If f(x) = |log₁₀ x|, then at x = 1

A. f(x) is continuous and f’ (1⁺) = log₁₀e 

B. f(x) is continuous and f’ (1⁺) = –log₁₀e 

C. f(x) is continuous and f’ (1^–) = log₁₀e 

D. f(x) is continuous and f’ (1^–) = –log₁₀^e

Answer 1

Option : (D)

(i) A function f(x) is said to be continuous at a point x=a of its domain, if  \(\lim\limits_{x \to a}f(x)=f(a)\)

Given :- 

f(x) = |log₁₀ x|