Math 1A: introduction to functions and calculus Sofia, 2013
Lecture 36: Worksheet
This worksheet was authored by Sofia 1
1 Differentiate the following functions: Level 1
a) f(x) = x+โx
b) f(x) = ex
c) f(x) = xโโx
d) f(x) = โ2x
e) f(x) = x+ sin(x)
2 Integrate the following functions: Level 1
a) f(x) = 5x4
b) f(x) = 1
c) f(x) = 3x2
d) f(x) = โ2
x3
e) f(x) = 3x2
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. T he later is of course much more
sophisticated. This entire LaTeX file was generated automatically.
3 Differentiate the following functions: Level 2
a) f(x) = (xโsin(x)) sec(x)
b) f(x) = โx3
c) f(x) = 1 โ3x
d) f(x) = eโxโx
e) f(x) = 1
x
4 Integrate the following functions: Level 2
a) f(x) = โ
2 sec2(1
x2)
x5โ
2 tan (1
x2)
x3
b) f(x) = exโexsec2(ex)
c) f(x) = 1โ
1
2โx
xโ
xโโx
x2
d) f(x) = โ1
x+ cos(x) + 1
e) f(x) = โ2
5 Differentiate the following functions: Level 3
a) f(x) = eโx
b) f(x) = 1
x3/2log(โx)
c) f(x) = xโlog(x)
d) f(x) = x4โ1
x3+ cos(x)
e) f(x) = x4+โxโex
