Math 101 – Calculus I
Final Exam Part I – June 2 2023
Instructors: Nilay Duruk Mutlubaş (Section A) and Şirin Kaya (Section B).
Full Name Student Number Signature
Time allowed for Part I is 80 minutes.
There are 4 problems worth a total of 30 points.
You MUST show your work and give explanations. No work equals no credit!
You must write your full name on ODD numbered pages.
Problem 1: (6 points)
Evaluate the limits given below.
ln(x2 + 1)
a) lim
x→0 x2
� �
−x ln(x2 + 1)
b) lim e −
x→0 x2
1
, Problem 2: (8 points)
√
The function f (x) = x − 1 is given.
a) Find the linear approximation to f (x) at the point x = 101.
√
b) Use the linear approximation you found in part a) to estimate the value of 102.
c) Is the value you found in part b) an overestimate or an underestimate? Explain why.
2
Final Exam Part I – June 2 2023
Instructors: Nilay Duruk Mutlubaş (Section A) and Şirin Kaya (Section B).
Full Name Student Number Signature
Time allowed for Part I is 80 minutes.
There are 4 problems worth a total of 30 points.
You MUST show your work and give explanations. No work equals no credit!
You must write your full name on ODD numbered pages.
Problem 1: (6 points)
Evaluate the limits given below.
ln(x2 + 1)
a) lim
x→0 x2
� �
−x ln(x2 + 1)
b) lim e −
x→0 x2
1
, Problem 2: (8 points)
√
The function f (x) = x − 1 is given.
a) Find the linear approximation to f (x) at the point x = 101.
√
b) Use the linear approximation you found in part a) to estimate the value of 102.
c) Is the value you found in part b) an overestimate or an underestimate? Explain why.
2
