Question

evaluate the equation. [sqrt(100+h)]-10/h with limit h->0

Answer 1

is the post correct? or is that a sqrt(10) instead?

Answer 2

rationalize the numerator by multplying top and bottom by
\[\sqrt{100-h}+10\]

Answer 3

(a-b)(a+b)=a^2-b^2

Answer 4

\[(\sqrt{100-h}+10)(\sqrt{100-h}-10)=(\sqrt{100-h})^2-10^2 \]
just like the formula

Answer 5

\[\lim_{h \to0} {\sqrt{100+h}-10\over h}\]

Answer 6

\[\lim_{h \to0} {\sqrt{100-h}-10\over h}\times \frac{\sqrt{100-h}+10}{\sqrt{100-h}+10}\]
\[=\frac{100-h-100}{h(\sqrt{100-h}+10)}\]\[=\frac{-h}{h(\sqrt{100-h}+10)}\] cancel

Answer 7

then replace \(x\) by \(10\)

Answer 8

is it 100+h or 100-h?

Answer 9

lol @satellite73 copied me

Answer 10

100+h

Answer 11

wait i copied him

Answer 12

you still do it in a very similar way
instead of -h on top you have+h and the same for the -h on bottom you have +h

Answer 13

but then how do i find the limit? @freckles

Answer 14

do you @satellite73 last step?

Answer 15

cancel out the factor h on top with the factor h on bottom

Answer 16

then plug in 0 for remaining h's

Answer 17

\[\lim_{h \to0} {\sqrt{100+h}-10\over h}\times \frac{\sqrt{100+h}+10}{\sqrt{100+h}+10} =\lim_{h \rightarrow 0}\frac{(100+h)-100}{h(\sqrt{100+h}+10)} \\=\lim_{h \rightarrow 0} \frac{h}{h(\sqrt{100+h}+10)} \]
do you see the h/h is 1 thing?

Answer 18

now just replace h with 0 and use order of operations

Answer 19

i got 1/20 is that correct?

Answer 20

yep because 10+10=20 :)
so we have 1/20
gj

Answer 21

@freckles thank you!

Answer 22

np