Could someone please help me? It's Calculus

Question

anonymous · Answer

$$\sqrt{x+1}-1/x$$
x= -0.001, -0.01, -0.1, 0, 0.001, 0.01, 0.1

anonymous · Answer

oh and lim x --> 0

anonymous · Answer

Is this
$$
\frac{ \sqrt{x+1}-1 }x
$$
?

anonymous · Answer

yes<3

anonymous · Answer

Take $$
f(x)=\sqrt{x+1}
$$

anonymous · Answer

The limit should be what in function of f(x)?

anonymous · Answer

well i know you're suppose to plug and chug those numbers but i kept getting 1 except when i was at 0

anonymous · Answer

$$
\lim_{x->0}\frac{f(x) -f(0)  }{x-0}=f'(0)
$$

anonymous · Answer

could you put that in table form?

anonymous · Answer

$$f'(x)=\frac{1}{2 \sqrt{x+1}}
\
f'(0)=\frac  12
$$

anonymous · Answer

$$
\left(
\begin{array}{cc}
 -0.001 & 0.500125 \
 -0.01 & 0.501256 \
 -0.1 & 0.513167 \
 0 & \text{Indeterminate} \
 0.001 & 0.499875 \
 0.01 & 0.498756 \
\end{array}
\right)
$$
You can see that the limits is approaching .5

anonymous · Answer

where did you get the 2

anonymous · Answer

Are you still here?

anonymous · Answer

no i got it, i had a brain fart, sorry for the stupid question lol