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CBSE Class 12-science Answered

2015,17 Find differentiable
question image
Asked by alanpeter9611 | 26 Feb, 2019, 02:30: AM
answered-by-expert Expert Answer
at x =1 , left side limit is given by begin mathsize 16px style limit as x rightwards arrow 1 to the power of minus of space x space equals 1 end style
 
at x = 1,  right side limit is given by begin mathsize 16px style limit as x rightwards arrow 1 to the power of plus of space 2 minus x space equals space 2 minus 1 space equals space 1 end style

hence at x=1, both left side limit and right side limit are equal, f(x) is continuous at x = 1 and differentiable.
 
at x =2, left side limit is given by begin mathsize 16px style limit as x rightwards arrow 2 to the power of minus of space 2 minus x space equals 2 minus 2 space equals 0 end style
 
at x = 2,  right side limit is given by begin mathsize 16px style limit as x rightwards arrow 2 to the power of plus of space minus 2 plus 3 x minus x squared space equals space minus 2 plus 6 minus 4 space equals space 0 end style

hence at x=2, both left side limit and right side limit are equal, f(x) is continuous at x = 2 and differentiable.
 
Answered by Thiyagarajan K | 27 Feb, 2019, 08:23: AM

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