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When x = 2e, [tex]\lim_{h \to 0} \frac{ln(x + h) - ln(x)}{h}[/tex] is ?

A. [tex]\frac{1}{2e}[/tex]
B. 1
C. ln(2e)
D. nonexistant

Respuesta :

LammettHash

Supposing you know about the derivative, notice that

[tex]\displaystyle\lim_{h\to0}\frac{\ln(x+h)-\ln x}h=\dfrac{\mathrm d(\ln x)}{\mathrm dx}=\dfrac1x[/tex]

so that when [tex]x=2e[/tex], the limit is equal to [tex]\dfrac1{2e}[/tex] and the answer is A.

BLUE0LIAM1

[tex]\lim_{h \to 0 } \frac{ ln(x + h) - ln(x) }{h} [/tex]

[tex] = \frac{d( ln(x)) }{dx} [/tex]

[tex] = \frac{1}{x} [/tex]

when x = 2e

[tex] = \frac{1}{2e} [/tex]

So , correct option is (A) 1/2e .

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