Question

Find the range of the function

Answer 1

@acxbox22 @amistre64 @CausticSyndicalist @dan815 @kropot72 @Lyrae @misty1212 @Preetha @rational @TheSmartOne @triciaal @whpalmer4 @ganeshie8 @mathmate

Answer 2

@myininaya Can you help me with this problem?

Answer 3

@sleepyjess

Answer 4

@mathmate any ideas?

Answer 5

startwith the domain is my first idea

Answer 6

let t = 2 sin(u)

dt = 2 cos(u) du

Answer 7

sqrt(4 - (2 sin(u))^2) 2 cos(u) du

sqrt(4(1 - sin(u)^2) 2 cos(u) du

2 cos(u) 2 cos(u) du

4 cos(u)^2 du

what do we know about this?

Answer 8

cos(u+u) = cos(u)cos(u) - sin(u)sin(u)

cos(2u) = cos^2 (u) - sin^2(u)

cos(2u) = 2cos^2 (u) - 1

cos(2u)/2 + 1/2 = cos^2 (u)

Answer 9

@amistre64 okay so how does this relate to my question?; there is no cos or sin in my question

Answer 10

its a u substitution in case integrating the original is difficult ....

Answer 11

its the integration that defines the function that you need the range for.

Answer 12

so how do i solve the range then

Answer 13

you integrate the function ... to start with. then you have something to analyse

Answer 14

i have no thrms memorized to help out, so working the process is all i got to go on

Answer 15

@amistre64 can u help me out w/ another ?

Answer 16

what are your thoughts?

Answer 17

i dont think its b or d @amistre64

Answer 18

what is the derivative of x^2?

Answer 19

oh, you DONT think its ... i agree with that assessment

Answer 20

2x

Answer 21

i was going to demonstrate why it was b ... but i misread your post lol

does f' tell us about the position of the points that f passes thru?

in other words?

if f' = 2x, do we know a specifc f for it?

Answer 22

**wasnt b .....

Answer 23

i dont understand what u mean by specific f @amistre64

Answer 24

what is the antiderivative of 2x?

Answer 25

\[\int 2x~dx\]

Answer 26

x^2+c

Answer 27

@amistre64

Answer 28

now, does x^2 + 3 pass thru the same points as x^2 -5?

Answer 29

they both have the same derivative, but the points they pass thru are not the same.

therefore we cannot say anything about what f passes thru if all we know is f'

Answer 30

does f pass thru 0? we dont know

Answer 31

so?

Answer 32

so a and c are our options ... which one does this remove?

Answer 33

can we say that f passes thru a specific point?

Answer 34

this removes a?

Answer 35

yep, only one option left

Answer 36

so c! yah @amistre64

Answer 37

can you help me with another problem?

Answer 38

@amistre64