Homework Statement
lim 2x/(sin3x)
x-> 0Homework Equations
lim sinx/x = 1
x->0
The Attempt at a Solution
is it correct to say the following:
lim 2/3 (sinx/x)
x-> 0
lim 2/3 (1)
x-> 0
Answer: lim 2x/sin3x = 2/3
x-> 0
Because it's on the book:
cos 2x(2)/3...
I don't know if I understand it.
If I have:
∫x3/√x dx
= ∫x3 - 1/2
= ∫x5/2
= (x5/2 + 1)/ 5/2 +1
= (x7/2)/7/2 + C
Simplyfying:
2x7/2/7 + C
Is this correct?
If not, what am I doing wrong?
Also, I am not sure how to proceed with ∫1/√x dx
If I have ∫1 dx:
= 1 + C
So for ∫1/√x dx I'll...
Thanks for the reply :)
But where does the sum sign come from?
Because even if it's 1 - y'
I will be still multiplying, as below:
-csc2 (x-y) . (1- y')
Homework Statement
2y = cot(x-y)
The Attempt at a Solution
2y' = -csc2 (x-y) . (1-y)(y')
Is it correct so far?
My book actually has
2y' = -csc^2 (x-y) + y' csc^2(x-y)
And I don't understand where that sum comes from. Am I supposed to apply the product rule? Because I tried and it didn't...
But isn't (∏)^2/12 = 2700 and 12/12 = 1
Wouldn't it be sort of equivalent to 2700 - sqrt of 3 (1.73) ?
That's what I am trying to understand. What's the difference if I work with 30 instead of ∏/6 ? Is it wrong? =/
Homework Statement
x3 - sin 2x
Find f'(∏/6)The Attempt at a Solution
f'(x) = 3x2 - 2 cos 2x
f(∏/6) = 2700 - 2 [ (√3/2) ] ---> from 2 [ cos(∏/6)]
answer: 2700 - √3
My book has the answer as (∏2 - 12)/12
I received a warning for excessive use of colors ??
I thought it was actually better for whoever was reading..to separate each problem by color since I was posting more than one.
I didn't do it because I was trying to decorate my post.
My bad.
:shy: Hi!
3. h(x) = cos [sec(5∏x)]
h'(x) = -sin [ sec(5∏x)][ tan (5∏x)] . 5∏
h'(x) = -5∏sin [ sec (5∏x) tan(5∏x)]
How about now?
What's the wrong with ∏ on nr 2 ? :/
Homework Statement
1. f(x) = 5 sin (8∏x)
2. g(x) = 4∏ [ cos (3∏x) sin (3∏x)]
3. h(x) = cos [sec (5∏x)]
4. Sketch the graph of each function on the indicated interval, making use of relative extrema and points of inflection.
f(x) = 2sinx + sin2x ; [0,2∏]
The Attempt at a...