Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
+1 vote
250 views
in Continuity and Differentiability by (42.5k points)
closed by

Show that ƒ(x) = |x-5| is continuous but not differentiable at x=5

1 Answer

+1 vote
by (44.7k points)
selected by
 
Best answer

Left hand limit at x = 5

\(\lim\limits_{x \to 5^-}\) |x-5| =  \(\lim\limits_{x \to 5}\) (5-x) = 0

Right hand limit at x = 5 

 \(\lim\limits_{x \to 5^+}\) |x-5| =  \(\lim\limits_{x \to 5}\) (x-5) = 0

Also f(5) = |5 – 5 |= 0 

As, 

 \(\lim\limits_{x \to 5^-}\) f(x) =  \(\lim\limits_{x \to 5^+}\) (5-x) = 0= f(5) 

Therefore, f(x) is continuous at x = 5 

Now, lets see the differentiability of f(x)

LHD at x = 5

Since, LHD ≠ RHD 

Therefore, 

f(x) is not differentiable at x = 5

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...