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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
- continuous for all values of x except x = 2 (correct)
- continuous for all values of x
- continuous for all at x = 0
- discontinuous at x = 0
- discontinuous at x = 2 (correct)
Lim (1 + x) ^ (1/x) is equal to
Lim (1 + x) ^ (1/x) is equal to
- none of their
- ∞
- π
- e (correct)
The function f(x) = |x| is
The function f(x) = |x| is
- continuous for all x (correct)
- discontinuous at x = 0 only
- discontinuous for all x except x = 0
- discontinuous for all x
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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