Math 1551A: Quiz 4
Friday, February 19th.
Problem 1. Consider the function:
f (x) =
x if x < 1
3x if x 1
Show that the function has no derivative at x = 1.
Problem 2. Compute
2
a) f (x) = x+x
x3
df
(x)
dx
1
b) f (x) = (3x2 + x )(x + 1)
for the functions b

Math 1551A: Quiz 2
Friday, January 29th.
Problem 1. Evaluate the following limit:
tan(4x)
.
x0 sin(6x)
lim
Proof: We can rewrite the limit as:
tan(4x)
sin(4x)
sin(4x) 6x
4
= lim
= lim
x0 sin(6x)
x0 sin(6x) cos(4x)
x0
4x sin(6x) 6 cos(4x)
lim
Now note that

Math 1551A: Quiz 3
Friday, February 5th.
Problem 1. Find the horizontal and vertical asymptotes of the function:
f (x) =
x1
.
x+5
Proof: When x = 5, the numerator is nonzero and the denominator is 0. This means that
the function will go to as x 5, so x =

Math 1551A: Quiz 5
Friday, February 26th.
Problem 1. Evaluate the derivatives for the following functions:
a) f (x) = esin x
b) g(x) = (x3 +
1
)2
cos(2x)
Problem 2.
a) Let F (x) = sin(g(x2 ) for x = 1 where g is a differentiable function such that g(1) =

Math 1551A: Quiz 6
Friday, Martch 4th.
Problem 1. Evaluate the derivatives of the following functions:
a) f (x) = sin1 (x2 + x)
b) f (x) = cos1 (sin1 x)
Problem 2. Consider the
function f (x) =
1
derivative of f (y) at y = 23 .
1 x2 dened for x [0, 1]. E

Math 1551A: Worksheet
Friday, March 4th.
Problem 1. Compute the derivatives of the following functions:
a) f (x) = sin(cos1 (sin(x).
b) f (x) = cos(sin1 (cos(x)
c) f (x) = log(x2 + 4x + 3)
d)f (x) = log(log(x)
e)f (x) = x log x x.
Problem 2. Let f (x) = l

Math 1551A: Worksheet
Friday, February 26th.
Problem 1. Compute the derivatives:
a) f (x) = sin(cos(sin(x).
ex
sin x
b) f (x) =
2
c) f (x) = ex sin x
d)f (x) =
x+
b
2x +
3x
e)f (x) = ax for some constants a, b = 0.
Problem 2. Consider a triangle ABC. The

Math 1551A: Quiz 1
Friday, January 22th.
Problem 1. Let f (x) = x2 + 16 and g(x) =
f g, and nd its range and domain.
1
.
x3
Find an expression for the function
2
2
1
1
+ 16. The domain will be x = 3 because x3 + 16 is well dened
Proof. f g =
x3
and nonneg

Math 1551A: Practice problems for Exam 1
Problem 1. Consider the functions f (x) =
x 4 and g(x) =
1
.
x+2
a) Find the domain and range of f .
b) Find the domain and range of g.
c) Find an expression for the function f g.
d) Find the domain of f g.
e) Find