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Winter 2019 Total Points: 55 10B Final Exam

Name:

PID:

- Print your NAME on every page and write your PID in the space provided above.

- Show all of your work in the spaces provided. No credit will be given for unsupported answers,

even if correct.

- No calculators, tablets, phones, or other electronic devices are allowed during this exam. You

may use one page of handwritten notes, but no books or other assistance.

Do not turn the page until instructed to do so.

Question Zero.

Follow the instructions on this exam and any additional instructions given during the exam.

1.

(6 pt) Determine whether the integral converges or diverges and evaluate it if it converges:

ZZ11 u1

2 du

ANAME:

10B Final Exam

Page 3 of 10

2.

(6 pt) The base of a solid object is the region in the fifirst quadrant (

x ≥ 0, y ≥

0) bounded by

y =

√9 x2 and the x-axis and y-axis. Cross-sections perpendicular to the

x-axis are squares.

Find the volume of the solid object.

10B Final Exam

Page 4 of 10

3.

(6 pt) Find the area of the region bounded by

y = xee2x, x = 0, x = 3, and y = 0.

ANAME:

10B Final Exam

Page 5 of 10

4.

6.

(8 pt) Use a trigonometric substitution to evaluate the defifinite integral:

Z01

1

√4

x2

dx

ANAME:

10B Final Exam

Page 8 of 10

7.

(6 pt) Find the solution of the difffferential equation that satisfifies

8.

(6 pt) A bacteria culture initially contains 500 cells and grows at a rate proportional to its size After

2 hours, the population increases to 2000 cells.

(a) Find a formula for the number of bacteria after t hours.

(b) When will the population reach 1 million (= 106 ) cells? Your answer may be written in

terms of a logarithm.

9.

(5 pt) Match the given difffferential equations to their direction fifields. For each difffferential equation

given below, write the UPPER CASE letter corresponding to the direction fifield in the blank

space provided.

(i)

dy

dx

= xy

(ii)

dy

dx

=

y

(iii)

dy

dx

= sin(x)

(iv)

dy

dx

= y + x

(v)

dy

dx

= sin(y)

(A) (B) (C)

(D) (E) (F)

A

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