Question

See attachment :-)

Answer 1

\(\bf \Large lim_{x\rightarrow0} \sqrt{x} \ \ ?\)

Answer 2

lim h-->0 sqrt(x+h) -sqrt(x) / h

Answer 3

and then i'm stuck

Answer 4

\[\lim_{\Delta x \rightarrow 0}\frac{ \sqrt{x+\Delta x}-\sqrt{x} }{ \Delta x }=\lim_{\Delta x \rightarrow 0}\frac{ \sqrt{x+\Delta x}-\sqrt{x} }{ \Delta x } \times \frac{ \sqrt{x+\Delta x}+\sqrt{x} }{ \sqrt{x+\Delta x}+\sqrt{x} } \]
\[= \lim_{\Delta x \rightarrow 0}\frac{ x+\Delta x-x }{ \Delta x \left( \sqrt{x+\Delta x}+\sqrt{x} \right)}= \lim_{\Delta x \rightarrow 0}\frac{ \Delta x }{ \Delta x \left( \sqrt{x+\Delta x}+\sqrt{x} \right)}=\lim_{\Delta x \rightarrow 0}\frac{ 1 }{ \left( \sqrt{x+\Delta x}+\sqrt{x} \right)}\]

Answer 5

\[=\lim_{\Delta x \rightarrow 0}\frac{ 1 }{ \left( \sqrt{x+\Delta x}+\sqrt{x} \right)}\]
is the last part. Do you see what you get?

Answer 6

0?

Answer 7

1/2

Answer 8

c

Answer 9

idk why i thought the limit would be a number or undefined

Answer 10

\[\lim_{\Delta x \rightarrow 0}\frac{ 1 }{ \left( \sqrt{x+\Delta x}+\sqrt{x} \right)}=\frac{ 1 }{ \left( \sqrt{x+0}+\sqrt{x} \right)}= \text{ ?}\]

Answer 11

1/2sqrt(x)

Answer 12

experience helps with these things. when you do and see them a few times, i'll stick.

Answer 13

you got it.

Answer 14

it'll, not i'll

Answer 15

thank you i took calc more than ten years ago, practice is long gone for limits...for some reason those didn't stick in my head

Answer 16

no worries, glad to help