MATH 110 - C01,C02 Midterm 2 November 20, 2019
Full Name: Student ID #:
** No calculators. 4 Pages. 50 minutes. **
(5) 1. Find the derivative y ′ of the curve implicitly defined by the equation:
2y + x cot y = x4
Answer: y ′ =
(5) 2. Find the following limit.
√
x2 + 3
3x − 4
lim
x→−∞
Answer:
Page 1
, (18) 3. Consider the following function f (x) and its derivatives:
2x + 3 2x + 2 4x + 2
f ( x)) = − 2 f ′ ( x)) = f ′′ ( x)) = −
x + 4x + 4 (x + 2)3 (x + 2)4
Answer each of the following showing your work below each question and placing
your final answers in the blanks provided.
(a) Find the domain D of the function. Answer:
(b) Find any y-intercepts of y = f (x) . Answer:
(c) Find any vertical asymptotes of y = f (x). Answer:
(Include any relevant limits in your work.)
Page 2
Full Name: Student ID #:
** No calculators. 4 Pages. 50 minutes. **
(5) 1. Find the derivative y ′ of the curve implicitly defined by the equation:
2y + x cot y = x4
Answer: y ′ =
(5) 2. Find the following limit.
√
x2 + 3
3x − 4
lim
x→−∞
Answer:
Page 1
, (18) 3. Consider the following function f (x) and its derivatives:
2x + 3 2x + 2 4x + 2
f ( x)) = − 2 f ′ ( x)) = f ′′ ( x)) = −
x + 4x + 4 (x + 2)3 (x + 2)4
Answer each of the following showing your work below each question and placing
your final answers in the blanks provided.
(a) Find the domain D of the function. Answer:
(b) Find any y-intercepts of y = f (x) . Answer:
(c) Find any vertical asymptotes of y = f (x). Answer:
(Include any relevant limits in your work.)
Page 2
