Question

-h

Answer 1

so, you are asked to find it with first principles?

Answer 2

well, you are asked to work it according to the limit definition instead of the more simpler rules

Answer 3

apply the formula, and the algebra works itself out

Answer 4

can we split it? or do we have to work it as one?

Answer 5

sqrt(c+h) + 2(c+h) - [sqrt(c)+2c]
----------------------------
h

the only issue you may have problems with is the sqrt, which can be dealt with by a conjugate

Answer 6

the fraction splits so splitting is just a part of the work

Answer 7

1/2sqrt(1) + 2 is not going to be 1/2 so i think you left or omitted something along the way

Answer 8

lets work it out again ...

Answer 9

sqrt(c+h) + 2(c+h) - [sqrt(c)+2c]
----------------------------
h



sqrt(c+h) + 2c +2h - sqrt(c)-2c
----------------------------
h



sqrt(c+h) - sqrt(c) +2h+2c -2c
----------------------------
h



sqrt(c+h) - sqrt(c) 2h
--------------- + ----
h h



sqrt(c+h) - sqrt(c)
--------------- + 2
h

the conjugate will help on the left term

Answer 10

(sqrt(c+h) - sqrt(c)) (sqrt(c+h) + sqrt(c))
----------------------------------
h (sqrt(c+h) + sqrt(c))


c+h-c
-------------------
h (sqrt(c+h) + sqrt(c))


h
-------------------
h (sqrt(c+h) + sqrt(c))


1
-------------------
(sqrt(c+h) + sqrt(c))

when h=0 this is just 1/2sqrt(c)

Answer 11

so, by the definition:

we have 1/2sqrt(1) + 2 at x=1

Answer 12

huh

Answer 13

oh ok