Find the rangeeeeeeeeee

Question

e.mccormick · Answer

$\sin(\sin x)+\cos (\sin x)$  Who thinks these up?  Hehe

OK, you know that the range of just $\sin x$ is [0,1].  However, that will be the domain of the outer functions.

terenzreignz · Answer

$$\Large * [-1 , 1]$$

e.mccormick · Answer

Oops!  yak, -1,1.  I am at work and having to answer othe quesions too.  LOL

anonymous · Answer

its impossible to find the range of this function

anonymous · Answer

http://www.wolframalpha.com/input/?i=range+of+sin%28sinx%29+%2Bcos%28sinx%29

e.mccormick · Answer

Don't trust wolframalpha.  It does not know what $\sqrt[3]{-1}$ means.

anonymous · Answer

i don't know how to proceed further

e.mccormick · Answer

It is graphable, so you have something to aim for just by looking at the graph: https://www.desmos.com/calculator/fgtlvxqx5t Now to see how to gt that mathematically.

anonymous · Answer

srry , but i didn't understand

e.mccormick · Answer

Is this considered trig, or calculus?

e.mccormick · Answer

If it is calculus, use derivative tests to find the min/max values.  For trig, it is a litle tricker.

anonymous · Answer

okay

e.mccormick · Answer

Okay?  So which is it?  What class are yu taking?  Are you expected to use calculus to solve this?

anonymous · Answer

+2

e.mccormick · Answer

According to that graph, the range is approximately $(-.301,1.414)$, but I bet your teacher will want exact values.  How they are found depends on what you are learning or have learned.

anonymous · Answer

u r right

anonymous · Answer

how can we draw a graph of sinx+cosx

e.mccormick · Answer

If you min/max it, you will have the local and absolute minimum and maximum points.  Plot those.  Then use the slope of the tangent line coming in and out to approximate where to draw based on if it is going up or down.

anonymous · Answer

okay

anonymous · Answer

i have a question , which i posted thrice a day
 i just want to confirm that the statement is true or false

anonymous · Answer

should i post it

e.mccormick · Answer

Yes, I saw that before.  I was not sure what the question meant, so I did not try to answer it.  You see, I am not used to saying 128 is a member of... and 496 is not a member of...

I can tell you that 128 is a power of 2.  $2^7=128$  But for factors... hmmm...

anonymous · Answer

okay 
no pblm
thank u

e.mccormick · Answer

However,t hat does mean you can factor 128 into a chain fo positive numbers.  
$2^8=256$ and $2^9=512$ so it does skip 496.

anonymous · Answer

can u solve it step by step
plsee

e.mccormick · Answer

128∈ {x : the sum all the positive factors of x is 2y } means:
128 is an element in x, such that the sum all the positive factors of x is 2y.  Is there supposed toeba an of in there?  sum of?  Probably.

$128= 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2$  So those are the positive factors of 128.  Therefore the sum of the positive factors is $2+2+2+2+2+2+2=14$  If $y=7$, then $2y=14$.  So it might be true, depends on what y is defined as.  

That is why I did not know how to answer that one.  I am not sure where they are getting the y from.

anonymous · Answer

okay

e.mccormick · Answer

496∉ {y : the sum of all the positive factors of y is 2y } means:

496 is not an element in y, such that the sum of all the positive factors of y is 2y.

This might be solveable.

$496 = 2\cdot 2\cdot 2\cdot 2\cdot 31 \therefore $ the positive factors.
$2+ 2+2+2+31=39$ and $2y=2(496)\implies 2y=992$ and $\because 992\ne 93$ the statement that 496 is NOT an element in this is true.

anonymous · Answer

93?

e.mccormick · Answer

Mistyped.  Meant 39.

e.mccormick · Answer

$993\ne 39$

anonymous · Answer

thank u

e.mccormick · Answer

So I am not sure on the first, but if you understand the math and symbols, I hope you can see why I say the second is true.