Mark M. answered 11/22/20
Retired math prof. Calc 1, 2 and AP Calculus tutoring experience.
Let f(x) = 2x
Then the given limit can be rewritten as limx→0 [ (f(x) - f(0)) / (x - 0)] = f'(0) = ln2(20) = ln2
Aisha M.
asked 11/21/20Lim 2x-1/x =
x-->0
A) 0
B) ln2
C) 1
D) 1/ln2
Side Note- the limit as x approaches 0 gets closer to 2 to the x power - 1 over x equals?
Mark M. answered 11/22/20
Retired math prof. Calc 1, 2 and AP Calculus tutoring experience.
Let f(x) = 2x
Then the given limit can be rewritten as limx→0 [ (f(x) - f(0)) / (x - 0)] = f'(0) = ln2(20) = ln2
Mike D. answered 11/22/20
Effective, patient, experienced math tutor who can help you succeed
Use L'Hopitals Rule
lim x>0 = lim x > 0 d/dx (2x - 1) / d/dx (x)
d/dx ax = ax ln a
So the derivative quotient is 2x ln 2 / 1, which tends to ln 2 as x > 0
So B
You can check this by substituting x = 0.0000001 into the original limit, you should get an answer close to ln 2
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