I know this is probably a common "sob story" but because of health issues and some circumstances, I need help solving these questions. If you could explain it but also give your final answers it would be very much appreciated ^0^
(there are 10 question! I also included answer choices so it would be hopefully easier~)
1.
If g(x)=5^x, then g'(2) is:
5
25In5
1/In5
5/In5
5 In5
2.
Which of the following are equal to pi/3?
arctan(tan pi/3)
arcos(sin -pi/6)
arcsin(sin ((2pi)/3)
3.
g(x)=x^3+2x-1 What is the slope of the tangent line to the curve g^-1 (x) at the pont (2,1)?
5
1/5
1
14
8
4.
The region in the first quadrant enclosed by the system of equations is rotated about the x-axis. The volume of the solid generated is:
y=0, x=5, and y=1/(sqrt(1+x))
pi In(6)
pi In(5)
pi In(4/3)
pi In(3/4)
pi In(10)
5.
∫(1)/(x^2 +4)dx=
arctan(2x)+C
1/2 arctan((1/2)x)+C
1/2 arctan(x)+C
In|x^2 +4| +C
1/2 In|x^2 +4|+C
6.
lim ((x-3)/(log3(x-1))
x->2
2
log3^2
-1/log3^2
infinity
does not exist
7.
The graph of f(x) is shown along with the line y=x
Assume that f^-1 (x) is defined by restricting f(x) to the domain a<x<b. Which of the following statements is false?
Graph (gyazo.com/c6d4871b661f5ed9207e169542ac4a79)
f^-1 (x) is a one to one function
f^-1 (x) has a domain of d<x<c
a=f^-1 (f(a))
(d/dx)(f^-1(x)) >=0
f^-1(c)=a
8.
The slope of the line normal to the curve e^x-x^3+y^2=10 at the point (0,3) is:
-1/6
1/6
6
-6
Undefined
9.
x
∫ t/(1+t^4) dt =
0
1/2arctan(x^2)
1/2arctan(x^4)
1/2In(1+x^4)
-1/2In(1+x^4)
1/2arcsin(x^2)
10.
Given (table: gyazo.com/daa1e2fb3a5c1b0bbe9afdccae6b56d7) what is a reasonable value for (d/dx)h^-1(x) evaluated at x=5?
3
1/3
1
-3
-1/3
Thanks for including the choices to each of your 10 questions for this test or assignment, but I cannot find your answers, therefore I am not able check them.
You do know that we don't just give answers to tests, that would be unjust to students that put in the effort to find the answers.
This isn't a test or assignment, I'm simply trying to catch up in my lesson as I have fallen behind due to health issues (I guess this is considered a review test? mock test? it's for studying, not a grade). There are no answers because I simply don't know how to solve these, that is why I am here for help. I was hoping you could explain them and give the answers so I could use these to study similar problems. I'm sorry for not being clear on my situation and I know I'm still at fault here. If you would like, I can attempt to solve these again before you help, but I think you would be quite disappointed as I am very behind and don't understand them well.
Thank you so much for responding to me and again, I am sorry for such an inconvenience.