Hello to all Mathematicians! Would you mind to help me here?
I've got some Problem and manage to solve some but still not sure on my answer though. Also, please check my answers if they were right or not. If its wrong then please correct me.
Legend:
indefinite integral = indefinite integral sign
sqrt. =square root sign followed by: ( )
^ = exponent
lim = limit
infinity = infinity sign
pi = pi sign
1. indefinite integral of sqrt.of ((1+2x)/1-2x)) dx
2. indefinite integral of (xsin(x))/cos^3(x) dx "where cos^3 (x) not cos(3x)"
3. lim x->-infinity ((x) sqrt. of (sin(2/x^2)))
4. lim x->1- ((pi/6)arcsin(x/2))^(1/arccos(x))
5. Using langrage equation find f(x)=3/2x if x(subscript:0) = 1
6. find the implicit function and fourth derivative function of: x^(3/4) + y^(3/4) =9
7. find the Max and Min of function y=3x + sqrt. of (1-x) in points [-5,1]
My answers:
1. -x-ln(|(-2x+1)|)+C
2. +C
3. e^(-1/2)
4. e^(pi/6)
5,6,7 ? i dont know how to solve it