MAT136 PRACTICE QUIZ 1
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PRACTICE QUIZ 1
Q1. The processing speed s in Ghz of a newly designed CPU depends on the processing speed s of the
previous model as in the following table.
s 
2.1 
2.3 
2.5 
2.9
s 
2 
2.1 
2.2 
2.3
What is a reasonable formula for the Taylor polynomial of degree 2 approximating s(s) at s = 2.3?
Q2. Suppose that
p(z) = 1 + 2(z − 1) − 
(z − 1)2 + 3(z − 1)3
is the degree 3 polynomial approximating f(z) at z = 1.
(a). Which of the following statements is true?
(1) f is increasing and concave up near 1.
(2) f is decreasing and concave down near 1
(3) f is increasing and concave down near 1
(4) f is decreasing and concave up near 1.
(b). What is the value of f\\\ (1)?
Q3. Suppose that f(t) is the current number of Netflix subscribers at day t of 2021. What is a practical description of the following formula?
1 365
f(t)dt
365 0
(1) The net change between the number of Netflix subscribers at day 0 and day 365.
(2) The total amount of of people that subscribed to Netflix in a year.
(3) The number of new Netflix subscribers recorded at day 365.
(4) The average daily number of Netflix subscribers for 2021.
Q4. Consider the following integral and suppose that f(t) is odd, f(1) = 1 and
1
t2 f\ (t)dt = 3.
What is the value of the following integral?
1
2tf(t)dt
一1
(1) 0
(2) -1
(3) 2
(4) -3
(5) 4
(6) -5
(7) Cannot be determined.
Q5. Suppose that u(t) represents the escape velocity in km/hour for a spacecraft orbiting a collapsing star as a function of the time measured in hours inside the spacecraft. Study the slope field of the differential
equation
du 1
dt 1 + sin(πt)
Assuming that u(0) = 
, after how much time it will become impossible for the spacecraft to escape the collapsing star? In other words, when is u(t) going to become infinitely large?
(1) After 30 minutes.
(2) After one hour.
(3) After one hour and a half.
(4) After two hours.
(5) Cannot be determined.
Q6. Consider the function
3
北
G(z) = et2 dt
2
北
(a). What is d(d)北(G) (z)?
(b). Compute the Taylor polynomial of degree 2 approximating G(z) at 0 and use it to approximate the
value of
G(z)dz.
一0.2
2023-02-08