Math 1A: introduction to functions and calculus Sofia, 2012
Lecture 36: Worksheet
This worksheet was authored by Sofia 1
1 Differentiate the following functions: Level 1
a) f(x) = xcos(x)
b) f(x) = x
c) f(x) = x−tan(x)
d) f(x) = 2x
e) f(x) = 1
x3
2 Integrate the following functions: Level 1
a) f(x) = 0
b) f(x) = 1
c) f(x) = 1 −1
x
d) f(x) = 1
x+ 1
e) f(x) = 3
1Written in the academic year 2003/2004, thanks to a grant from the Harvard Provost together with Johnny
Carlsson,Andrew Chi and Mark Lezama. Sofia was a chat bot which would use computer algebra systems
to solve calculus problems while chatting, similar to Wolfram Alpha now. The later is of course much more
sophisticated. This entire LaTeX file was generated automatically.
3 Differentiate the following functions: Level 2
a) f(x) = x4+x+ tan(x)
b) f(x) = −x4+x+ tan(x)
c) f(x) = (x−4)x3
d) f(x) = (x+ cos(x)) cot(x)
e) f(x) = −2exx
4 Integrate the following functions: Level 2
a) f(x) = e−x−e−xx−sec2(x)
b) f(x) = 1
x−cos(x) + 1
c) f(x) = 1
d) f(x) = sec(x)
x+2 −
xsec(x)
(x+2)2+xtan(x) sec (x)
x+2
e) f(x) = 2x
5 Differentiate the following functions: Level 3
a) f(x) = e−x(xcos(x) + tan(x))
b) f(x) = √xlog(x)
c) f(x) = −√xcsc(x)
d) f(x) = e−xx−log(x)
3x
e) f(x) = e−x
9x
