# sqrt

1. ### volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2 )

By using spherical coordinates , find the volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2 ) , below by plane z = 0 ... Calculus III - Spherical Coordinates I'm having problem finding my Φ .... Here's my diagram ... The shaded part represent the volume...
2. ### (sqrt(n)/(n+100))-(sqrt(n+1)/(n+101))

Not sure if this is the right thread to post this, but I got this kind of as home work from calculus, so basically the thing looks like this (sqrt(n)/(n+100))-(sqrt(n+1)/(n+101)) , wolfram says the answer should be n = sqrt(40001)/2 - 1/2. Anyone got any ideas?
3. ### integrate 1/ sqrt rt ( 1-e^(2x) ) using trigonometry substituition

how to integrate 1/ sqrt rt ( 1-e^(2x) ) using trigonometry substituition ? How should I start ? i know that for sqrt rt (a^2 -x^2 ) , i should use asinθ
4. ### integrate 1/( x ( sqrt rt (x2 -1 ) ) ) from √2 to 2

i gt it = arc sec x , then i sub √2 and 2 inside , i gt an error , why is it wrong ?
5. ### integrate x / sqrt rt (4- (3x^4) )

the ans is π/6√3 , but my ans is π/3√3... which part is wrong ?
6. ### 2nd partial derivative of [sqrt of x^2 + y^2] for x

Hi Folks, The first partial derivative of the [sqrt of x^2 + y^2] = x/[sqrt(x^2 + y^2)]. That I can see is obvious. I used the product rule to get the 2nd partial derivative. Let f(x) = x, g(x) = (x^2 + y^2)^(-1/2) [[x squared + y squared] raised to the -1/2 power.] Since f(x)g'(x) +...
7. ### Integral of x^2 sqrt (ax^2 + b x + c) dx

Integral number 287 is similar to 286: \int x^2 \sqrt {ax^2 + b x + c} \ \mathrm d x I haven't found a useful substitution: z = x^2, \frac 1 u and \sqrt {ax^2 + b x + c} all seem to lead nowhere. I have also tried splitting it into u = x, \mathrm d v = x \sqrt {ax^2 + b x + c} but the algebra...
8. ### Integral of x sqrt (ax^2 + b x + c) dx

We're up to number 286 in Fiendish Integrals for Masochists ... \int x \sqrt{a x^2 + b x + c} \ \mathrm d x The posted solution is: \frac {\left({\sqrt {a x^2 + b x + c} }\right)^3} {3 a} - \frac {b \left({2 a x + b}\right) \sqrt {a x^2 + b x + c} } {8 a^2} - \frac {b \left({4 a c -...
9. ### Integral of 1 / (x sqrt (ax^2 + b x + c)) dx

I'm working my way through a series of ever tougher integrals. I'm stuck at no. 283: \int \frac {dx} {x \sqrt {a x^2 + b x + c} } ... and there are some further even tougher ones. I understand that it is supposed to evaluate to: - \frac 1 {\sqrt c} \ln \left({\frac {2 \sqrt c \sqrt {a x^2 +...
10. ### square root problem, wtf??

Hey! I need help with this task: 4−9x=9x−2 i'm supposed to find out att what values of x the equation is defined, in other words the answer is supposed too look like this: a<x<b. I alreade know that the equation is not defined if x<0. I have tried it a million times but i just can't get it...
11. ### integral with sqrt in denominator

Hello! Please, what should I do with the sqrt in the denominator? \int \frac{dx}{\sqrt{2+3x-2x^2}} Please, help someone!!!! Many thanks!
12. ### Solve sevral simple inequalities with modulus and sqrts.

Task 1: abs(7-3x) + 4x > 5 Task 2: sqrt(7-3x) <= x -1 Task 3: sqrt(5-2x) > 1 - x Task 4: x^2*(1 + 4x^2) < abs(x - 2x^2) + 6 + 4x^3
13. ### Limit w/ Sqrt function in numerator

\lim_{x \to inf} \frac{\sqrt {2 + 9x^2}}{5+2x} I don't really know how to algebraically simplify the top. I tried to do the divide by x trick (since x is the variable with the greatest denominator available. I'm not really sure how to get the LaTeX going for the multiple fraction bars yet, but...
14. ### Why does sqrtAB over B become sqrt AB

How do I make a post solved please I know from using practical values this does happen but I don't understand were the extra B is cancelled out I will try again with LaTex THIS IS NOT CORRECT perhaps some could show me what is wrong frac\{\sqrt{AB}{B} I still can not work LaTex out ...
15. ### transposing with sqrt and sqr

Goodday , may someone please help with this . I would like to isolate the h on the other side of the = . Exchange it with the q. q=d^2*(sqrt(2*g*h))*pi/4 Thanks Rob
16. ### Solve ln(3*sqrt(x)) = sqrt (ln x)

I'm hitting a wall on this. It's: ln3 + 1/2*ln x = sqrt (ln x) That's where I hit the wall. ln 3 + 1/2*u = u^1/2 If I square both sides it gets to be a mess.
17. ### [Integration] Don't know how integrate with sqrt and a square

Don't know how to integrate this. 2 \sqrt{1-x^2} It says, hint: use x=sin(\theta)
18. ### multiplying with powers and sqrt

How would you combine this? x^(3/2) * sqrt(x+1) = ? Thanks,
19. ### proof that sqrt(ab-ac)=a sqrt(b-c)

Proof that: sqrt(ab-ac)=asqrt(b-c) without the use of substitution Thx
20. ### Infinite Sum, involving sqrt and a+b+c

Hi Forum! I've found this strange question, which asks the following: If \sqrt{10+\sqrt{10+...}}= (a+\sqrt{b})/c Find a+b+c Now, this question was in a quadratics exam. The solution given is quite simple, but it doesn't really seem to make sense. Can someone help? Thanks