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Questions and Answers
The function f(x) = (1 + x if x ≤ 2) and f(x) = (5 - x if x > 2), is
The function f(x) = (1 + x if x ≤ 2) and f(x) = (5 - x if x > 2), is
Lim (1 + x) ^ (1/x) is equal to
Lim (1 + x) ^ (1/x) is equal to
The function f(x) = |x| is
The function f(x) = |x| is
Let f(x) = Sin x when x≠0 then the value of f(0) so that f(x) becomes (continuous at x = 0)
Let f(x) = Sin x when x≠0 then the value of f(0) so that f(x) becomes (continuous at x = 0)
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Study Notes
Limits and Continuity
- Limit of (1+x)/y as x approaches 0 is 1
- Limit of (1/x) as x approaches 0 is undefined
- Limit of e^x as x approaches 0 is e^0 = 1
- Limit of [(1+x)^x] as x approaches 0 is e
- Function f(x) = cos x for x >= 0 and -cos x for x < 0 is continuous for all x except x = 0
- Function that is (1+x) for x<=2 and (-5+x) for x>2 is continuous for all values of x except x=2
- Function f(x) = |x| is continuous for all x except x =0
- It is discontinuous at x = 0 only
- Function f(x) = sin x / x when x is not equal to 0 will be continuous at x = 0 if f(0) = 0
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Description
Test your understanding of limits and continuity with this quiz. Explore various limits, including undefined limits and continuous functions. Assess your knowledge on key concepts and their applications in calculus.
