Exam 2 Study Guide
high school geometry
area of rectangle
area of circle
surface area of sphere
volume of sphere
volume of cone
volume of box or cube
Chapters 1 and 2 as covered in the
Exam 1 Study Guide
.
Chapter 3
definitions
e
log
_{a}
u, ln u
sin u, cos u, tan u
sin
^{-1}
u, cos
^{-1}
u, tan
^{-1}
u
sinh u, cosh u, tanh u
sinh
^{-1}
u, cosh
^{-1}
u, tanh
^{-1}
u
derivatives (with proofs) of the following types of expressions:
c, x, cu, u+v, u-v, uv, 1/v, u/v
u
^{n}
, e
^{u}
, a
^{u}
, u
^{v}
composite functions, inverse functions
log
_{a}
u, ln u
sin u, cos u, tan u
sin
^{-1}
u, cos
^{-1}
u, tan
^{-1}
u
sinh u, cosh u, tanh u
sinh
^{-1}
u, cosh
^{-1}
u, tanh
^{-1}
u
identities:
cos
^{2}
u + sin
^{2}
u = 1
cosh
^{2}
u - sinh
^{2}
u = 1
1 + tan
^{2}
u = sec
^{2}
u
1 - tanh
^{2}
u = sech
^{2}
u
reading graphs
recognizing limits as derivatives
computing certain limits by rewriting them in terms of derivatives
equations of tangent lines and normal lines
implicit differentiation
logarithmic differentiation
rates of change of quantities with units, in physics, economics, or the social sciences; for example: velocity, population growth, etc.
higher derivatives; for example: acceleration, jerk.