Q79.Let f(x) = {(x k, x = 2 The value of k for which f is continuous at x = 2 is (1) e−2 (2) e (3) e−1 (4) 1
What This Question Tests
The question tests the concept of continuity of a function at a point by evaluating a limit of an indeterminate form (1^infinity) using L'Hopital's rule, interpreting the function as f(x) = (x-1)^(1/(x-2)) for x!=2 and f(2)=k.
Concepts Tested
Formulas Used
lim_{x->a} f(x) = f(a) for continuity
lim_{x->a} (f(x))^(g(x)) = e^(lim_{x->a} g(x)ln(f(x)))
L'Hopital's Rule
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📋 Question Details
- Chapter
- Limits & Continuity
- Topic
- Continuity of a function at a point
- Year
- 2018
- Shift
- 15 Apr Shift 2 Online
- Q Number
- Q79
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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