Question

lim h -> 0
(cos( (pi/2) + h) - cos( (pi/2) ) ) / h

Answer 1

@RadEn

Answer 2

looks like it is the defined of derivative of cos(x), right ?

Answer 3

yeah

Answer 4

nah, the derivative of cos(x) = - sin(x)
:)

Answer 5

yep :)

Answer 6

so, the answer is -sin(x)

Answer 7

but the answer at the back was -1

Answer 8

@RadEn

Answer 9

opppss.. yes, it wants find up the value of (cos(x))' for x=0
we have (cos(x))' = -sin(x)
now put x=0, it is -sin(0) = 0

hmm... i dont know whcih parts i made mistake

Answer 10

so u dont know how the answer is -1 then?

Answer 11

well, i will try again... miss all above :)

Answer 12

use the identity :
cosA - cosB = -2sin(((A+B)/2)sin((A-B)/2)

Answer 13

wait let me interpret what you just typed

Answer 14

so,
cos( (pi/2) + h)-cos(pi/2) = -2sin((pi/2)+h+pi/2)/2)sin(((pi/2)+h-pi/2)/2)
= -2sin(pi+h)/2)sin(h/2)
= -2sin(pi/2+h/2)sin(h/2)
remember the identity :
sin(pi/2+x) = cos(x)
therefore, it can be
= -2cos(h/2)sin(h/2)

Answer 15

that's just for the numerator

Answer 16

i'll just ask my teacher tomorrow you use to many parenthesis i cant understand :\

Answer 17

we will forward its answer ...

Answer 18

can you help me with the next question?

Answer 19

didnt u want finish it ...

Answer 20

i'll just ask my calc. teacher tomorrow, he did a shorter version of it :)

Answer 21

can you help me with another question? :)

Answer 22

i will try :)