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
2 answers
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.
Thank you so much for responding to me and again, I am sorry for such an inconvenience.