Answer:
no solution
Step-by-step explanation:
infinitely many solutions
Answer:
Step-by-step explanation:
a)
![\int\limits^2_1 {\frac{1}{x(lnx)^p} } \, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5E2_1%20%7B%5Cfrac%7B1%7D%7Bx%28lnx%29%5Ep%7D%20%7D%20%5C%2C%20dx)
this can be done by substitute lnx = u
dx/x = du
When x =1, u =0 and when x =2, u = ln 2
So integral = ![\int\limits^{ln2} _0 {du/u^p} \\\=\frac{u^{-p+1} }{-p+1}](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7Bln2%7D%20_0%20%7Bdu%2Fu%5Ep%7D%20%5C%5C%5C%3D%5Cfrac%7Bu%5E%7B-p%2B1%7D%20%7D%7B-p%2B1%7D)
We find that this integral value is not definid for p =1
Hence for values of p other than 1, this converges.
When we substitute limits
![\frac{1}{1-p} ((ln2)^{1-p} -1)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1-p%7D%20%28%28ln2%29%5E%7B1-p%7D%20-1%29)
and converges for p ≠1
b) ![\int\limits^1_0 {lnx}/x^p \, dx \\\int \frac{\ln \left(x\right)}{x^p}dx=\frac{1}{-p+1}x^{-p+1}\ln \left(x\right)-\frac{x^{-p+1}}{\left(-p+1\right)^2}+C](https://tex.z-dn.net/?f=%5Cint%5Climits%5E1_0%20%7Blnx%7D%2Fx%5Ep%20%5C%2C%20dx%20%5C%5C%5Cint%20%5Cfrac%7B%5Cln%20%5Cleft%28x%5Cright%29%7D%7Bx%5Ep%7Ddx%3D%5Cfrac%7B1%7D%7B-p%2B1%7Dx%5E%7B-p%2B1%7D%5Cln%20%5Cleft%28x%5Cright%29-%5Cfrac%7Bx%5E%7B-p%2B1%7D%7D%7B%5Cleft%28-p%2B1%5Cright%29%5E2%7D%2BC)
So not converging for p =1
But ln x is defined only for x >0
So integral 0 to 1 makes this integral not valid and hence not convergent.
Answer:
40 gold notebooks
Step-by-step explanation:
5:3 gold notebooks to red notebooks so using this we can set up a proportion
5 x
-- = ---
3 24
cross multiplying
3x = 120
x= 40
so there are 40 gold notebooks if there are 24 red notebooks
3x+y=9.....i
3x-5y=15...ii
subtracting ii from i we get
6y=-6 so y=-1
x=10/3
Answer:
y = 1250
Step-by-step explanation:
![y = 10 * 5^{x}](https://tex.z-dn.net/?f=y%20%3D%2010%20%2A%205%5E%7Bx%7D)
x = 3
y = y
Substitute x into equation
![y = 10 * 5^{3}](https://tex.z-dn.net/?f=y%20%3D%2010%20%2A%205%5E%7B3%7D)
Simplify ![5^{3}](https://tex.z-dn.net/?f=5%5E%7B3%7D)
y = 10 * 125
y = 1250
Hope this helps :)