Math 1432
*Reserve a seat for Test 2.
* Take Practice Test 2.
* Solve the problems on the review sheet posted on my website.
*If you have never done so – go to CASA testing center for
fingerprint/picture process.
*Double check your reserved time. Plan to be at the testing center earlier
than your reserved time. If you’re more than 10 min. late, they will not
take you in. Bring your Cougar ID with you.
* No make ups! If you miss your reserved spot, try to reschedule online.
Generally, there are no open seats for the last days, so you may not be able
to reschedule. In that case, you will get 0 on this test and final replaces one
missed test.
* No calculators.
POPPER06
Q#
d x2
5
dx
3x
1
(
f
) ' (b)
Q# If f (a) = b,
Test 2: Sections 7.1 – 8.2
KNOW:
Formulas for derivatives:
Inverse functions
ln u and loga u
eu and au and (u)v
arctan u and arcsin u
sinh u and cosh u
Integration:
u-sub (and any other calc 1 techniques)
integrals for any of
o ln u and loga u
o eu and au
o arctan u and arcsin u
o sinh u and cosh u
integration by parts
Exponential growth/decay problems
Some problems:
1.Is the function f (x) = x3 + 3x invertible? If so, find the derivative of the
inverse of f at 14. Note that f (2) = 14. What is the equation of the
tangent line to the curve f 1 at x= 14?
2.Give an equation for the tangent line to the graph of
g x
ln 4 x 1 2 e x at the point where x = 0.
3.Solve the differential equation:
2y' y
.
y' 0 5
4.Suppose a culture of bacteria is growing in such a way that the change
in the number of bacteria is proportional to the number present. The
number of bacteria double every 20 minutes and there are currently 100
bacteria in the culture. How many bacteria were present 55 minutes
ago?
d x2
e
dx
4x
d
log 3 2x 2
dx
d
arctan 5 x
dx
d
ln tan 2x
dx
d
5
dx
4x
d
arcsin 5 x 2
dx
d
ln 6 x 2
dx
POPPER06
Q#
d
cosh 7 x 2
dx
3
d
3x 2
dx
1
4x 2
sec2 x
dx
tan x 25
7
225
3x 1
2
dx
e
x
dx
x
ex
16
e2 x
dx
5 x sin 2x dx
2xe 6 x dx
2 x ln 10 x dx
sin 9 x
4
cos 9 x
2
dx
POPPER06
Q#
ln 3x 2
x
dx