Question

find in terms of the constant a.
lim h of 0 5(a+h)squared - (5a)squared
____________________________
h

Answer 1

First expand

\[\rightarrow \frac{5(a^{2}+2ah+h^{2}) - 5a^{2}}{h}\]
combine terms
\[\rightarrow \frac{10ah +5h^{2}}{h}\]
Factor out a h from numerator
\[\rightarrow \frac{h(10a +5h)}{h} = 10a +5h\]
Now take limit as h->0
\[\lim_{h \rightarrow 0} 10a+5h = 10a\]

Answer 2

is that (5a)^2
or 5a^2?

Answer 3

5a squared

Answer 4

\[\lim_{h \rightarrow 0}\frac{5(a^2+2ah+h^2)-(5a)^2}{h}=\lim_{h \rightarrow 0}\frac{5a^2+10ah+5h^2-25a^2}{h}\]
\[=\lim_{h \rightarrow 0}\frac{-20a^2+10ah+5h^2}{h} DNE\]

Answer 5

is the square just on the a
or is it on the whole thing
because it looks like it is on the whole thing to me

Answer 6

the whole thing

Answer 7

in that case, the first part should be ....(5(a+h))^2

Answer 8

cow we aren't doing derivatives
we are just finding limits

Answer 9

you will get 50a as the answer instead of 10 a
...
looks like the definition of the derivative to me

Answer 10

i believe anyways

Answer 11

it reads 5 times a plus h squared minus 5a squared over h
it says find in terms of the constant a

Answer 12

\[\frac{5(a+h)^2-(5a)^2}{h} ?\]

Answer 13

yes

Answer 14

or
\[\frac{(5(a+h))^2-(5a)^2}{h}\]

Answer 15

without () around 5a. NOT the second one you typed

Answer 16

well in that case as myininaya showed above...the limit does not exist or is undefined,

Answer 17

it doesn't make sense to me though...usually the coefficients would be the same, you just replace a with (a+h)

.... f(a+h) - f(a) / h

Answer 18

ok. THANK YOU GUYS! I have another one for you. I have the answer but Im not sure if its correct lim h of 0 the square root of (3+h) - the square root of 3 all over h. I got 1. is that wrong?

Answer 19

yeah the answer should be 1/(2sqrt(3))

Answer 20

when you multiplied by conjugate, make sure you do it on top and on bottom

Answer 21

the answer DNE was incorrect

Answer 22

if you want the right answer if you need to tell exactly what the problem is