Question

When x = 2e, %7D" id="TexFormula1" title="\lim_{h \to 0} \frac{ln(x + h) - ln(x)}{h}" alt="\lim_{h \to 0} \frac{ln(x + h) - ln(x)}{h}" align="absmiddle" class="latex-formula"> is ?
A. $\frac{1}{2e}$
B. 1
C. ln(2e)
D. nonexistant

Answer 1

Supposing you know about the derivative, notice that

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

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

Answer 2

$\lim_{h \to 0 } \frac{ ln(x + h) - ln(x) }{h}$

$= \frac{d( ln(x)) }{dx}$

$= \frac{1}{x}$

when x = 2e

$= \frac{1}{2e}$

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

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