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Hi Max,

I am not very good at limits so this is probably not correct but this is my best 'guess' :)

I have no idea why this is a calculus question... 

I am very happy for you to comment :)

\(\displaystyle\lim_{n\rightarrow \infty}\sum^{n-1}_{k=1}\dfrac{n}{4n^2+k^2}\\~\\ =\displaystyle\lim_{n\rightarrow \infty}\left[ \dfrac{n}{4n^2+1}+\dfrac{n}{4n^2+4}+\dfrac{n}{4n^2+9} \dots \dfrac{n}{4n^2+(n-1)^2}\right]\\ \text{Divide numerator and denominator by }\frac{1}{n^2}\\~\\ =\displaystyle\lim_{n\rightarrow \infty}\left[ \dfrac{(1/n^2)n}{4+1/n^2}+\dfrac{(1/n^2)n}{4+4/n^2}+\dfrac{(1/n^2)n}{4+9/n^2} \dots \dfrac{(1/n^2)n}{4+(n-1)^2/n^2}\right]\\ =\dfrac{0}{4}+\dfrac{0}{4}+\dfrac{0}{4} \dots \dfrac{0}{5}\\ =0 \)

The numerator stays zero and the denominator starts at 4 and creeps up to 5 but overall each fraction looks like 0 to me.

A small ball is launched directly upward from ground level with an initial velocity of 12 m/s. What is the ball's maximum height above the ground?

\(mgh=\frac{1}{2}mv^2\)

\(\large h=\frac{v^2}{2g}\)

\(\Large h=\frac{\frac{12^2m^2}{s^2}}{2\times 9.81\frac{m}{s^2}}\)

\(\large h=7.339m\)

!

I think I can do this problem, but I'm not the best at these so it could be wrong.

Using 9.8 m/s² as the approximation for gravity:

acceleration function: →  h''(t) = -9.8

velocity function: →         h'(t) = -9.8t + 12

position function: →         h(t) = -4.9t² + 12t

I didn't explain all the steps I did there because I don't know if my way of doing it is the best way; it's just the only way I know how to do it. So I don't want to confuse you any if my way is not the way you've been taught to do it.

We need to find the values of t where the velocity, h'(t) = 0. The velocity will be zero right at the max height.

0 = -9.8t + 12

-12/-9.8 = t

60/49 = t

So at t = 60/49, the velocity is 0. So let's find the position, h(t), when t = 60/49.

h(60/49) = -4.9(60/49)² + 12(60/49)

h(60/49) = -4.9(3600/2401) + 720/49

h(60/49) = -360/49 + 720/49

h(60/49) = 360/49 ≈ 7.347 meters

if x>0, x^2=2^64 and x^x=2^y what is the value of y? 

\(x^2=2^{64}\)              square root

\(\sqrt{x^2}=\sqrt{2^{64}}\)       calculate

\(x=2^{32}\)               result for x

\(\large x^x=2^y\)            output equation.  x-value

\(\large x^x=(2^{32})^{2^{32}}=2^{32\times 2^{32}}=2^{2^5\times 2^{32}}=2^{2^{37}}=2^y\)

\(\large2^{2^{37}}=2^y\)          output equation. x is used

If the basis of two powers is equal, the exponents are equal.

\(\large y={2^{37}} \)

\(y=137438953472\)

  !

\(\large x^x=2^y\)    output equation. x and y used

\(\Large(2^{32})^{(2^{32})}=2^{137438953472}\)    x and y used. calculate

\(\large32\times2^{32}=137438953472\)  q.e.d

  !

1. Multiplying a positive and a negative equals a negative

\(y=f\times (-X)\)

2. The final solution for y is

\(y=-fX\)

3. Answer

\(y=-fX,f\in\mathbb{R},X\in\mathbb{R}\)

sadly dodos are extinct...T^T i cri

asian food...especially sushi and jaepchae! <3

Oops. Sorry for giving the wrong information.

I have just woke up and my brain is probably not working properly.

yo you can't divide by 0 bruh

-3 - -4 - 5

= -3 + 4 - 5 | Subtracting a negative number is adding (-1 * negative number)

= 1 - 5

= -4

No it isn't max it is undefined.

lim x tend to 0 from positive side is infinity

lim x tends to 0 from the negative side is - infintiy

put them together and it makes no sense, you cannot divide by 0 !

When you reflecting a point in the x - axis, you multiply -1 to the y - coordinates to get the coordinates of the new point. same as a line.

Coordinates of D = (4 , -3)

Therefore Coordinates of D' = (4 , -3*-1) = (4 , 3)

Coordinates of F = (-2 , 4)

Therefore coordinates of F' = (-2 , -1 * 4) = (-2 , -4)

x² would be 2³² times 2³² because 2³² times 2³² equals 2⁶⁴  then x would be plus or minus 2³² but since x is positive it would be plus 2³² so the question would be asking what is 2^y if it equals x squared 32 is 2⁵ than you can say 2³² squared is 2^{2^37} because (2^{^2^5})^{^2^32} is 2^{2^37} therefore the value of y would be 2³⁷ 

When the number is just a number, i.e. no signs, e.g.: 5, 7, 0.5, they are positive

When the number contains negative sign, e.g.: -1, -2/3, -\(\pi\), they are negative

- 2x + 15 = - 9 | rearrange

15 - 2x = -9 | multiply -1

2x - 15 = 9 | + 15

2x = 24 | /2

x = 12

Hi asinus.

If you are English then a neddy is a donkey

but if you are Australian then a neddy is a race horse.

Somehow I think you mean a donkey :))

Yes i can see the attraction :)

I like many animal but one favourites is the Australian Galah.

I used to have one as a pet when I was a child.

I love dodos xD

30 + (-50) - 20 <-- the brackets are unnecessary

= 30 - 20 + (-50)

= 10 + (-50)

= 10 - 50

= -40

Same as hectictar's answer.

:D

Use division actually.

'how many time does 7 go into 21 and 49'

Do \(21 \div 7 = 3\\ 49 \div 7 = 7\)

Finish!!

(30) + (-50) - (20)

= 30 - 50 - 20

= -40

Use logarithms.

x^2 = 2^64 | Take natural log both sides

2 ln x = 64 ln 2 | /2

ln x = 64 ln 2 / 2 | e^ both sides

x = e^(64ln 2/2) = 2^(64/2) = 2^32

x^x = 2^y | natural log again......

x ln x = y ln 2 | substitution

2^32 ln 2^32 = y ln 2 | log property

32 * 2^32 ln 2 = y ln 2 | multiply

2^37 ln 2 = y ln 2 | / ln 2

y = 2^37

thank you 

how many time does 7 go into 21 and 49 i would use a calcuator but dont have one 

Just type 'pi' in the calculator. It understands.

Top row second column from left.