Transcendental equations: derivatives, integrals, limits,
I have to help teach this class tomorrow for my Senior Seminar Math class. The lesson is over Exponential and Logarithmic Functions and L'Hospital's Rule. I have all the problems needed to review this lesson, but i can not solve any of them. My teaching partner and I have had schedule conflicts and we are now on our own. It is late starting but any help or advise would be greatly appreciated. I have not had calculus in 5 years.
1. y=√(2)*e^(√(2)x) y` =?
2. y=ln(sec^(2)x) y`=?
3. y=9^(2t) y`=?
4. y=[2(x^2+1)]/[√(cos 2x)] y`=?
5. ∫ e^t * cos(3e^t - 2) dt
6. ∫(top: π/6, bottom: -π/2) (cos t)/(1-sin t) dt
7. ∫ [ln(x-5)]/(x-5) dx
8. ∫(top: e, bottom: 1) (1/x) * (1+ 7 ln x)^(-1/3) dx
9. ∫(top:3, bottom: √3) dt/(3+t^2)
Solve for Y
10. 3^y = 3 ln x y=?
11. lim (x→0) (3^x - 1) / x
12. lim (x→0) (4 - 4e^x) / xe^x
13. lim (y→0+) e^(-1/y) ln y
My partner has the other 13 problems and his are basically the same. I know this is a lot but any help with any of these would be greatly appreciated.