Q80.Let ๐: ๐ โ๐ be a function defined as 5, ๐๐ ๐ฅโค1 ๐+ ๐๐ฅ, ๐๐ 1 < ๐ฅ< 3 ๐๐ฅ= ๐+ 5๐ฅ, ๐๐ 3 โค๐ฅ< 5 30, ๐๐ ๐ฅโฅ5 Then ๐ is: (1) continuous if ๐= - 5 and ๐= 10 (2) continuous if ๐= 0 and ๐= 5 (3) not continuous for any values of ๐ and ๐ (4) continuous if ๐= 5 and ๐= 5
What This Question Tests
This question tests the understanding of continuity of a piecewise function by setting up equations for limits at the transition points and solving them for 'a' and 'b'. It reveals that such 'a' and 'b' do not exist for the function to be continuous.
Concepts Tested
Formulas Used
lim (x->c-) f(x) = lim (x->c+) f(x) = f(c) for continuity
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๐ Question Details
- Chapter
- Limits & Continuity
- Topic
- Continuity of piecewise functions
- Year
- 2019
- Shift
- 09 Jan Shift 1
- Q Number
- Q80
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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