CALCULUS EXAMPREP FULLY SOLVED EDITION
WITH COMPREHENSIVE MATHEMATICS
QUESTIONS
◉let f b a function that is continuous on the closed interval [2,4] with
f(2)=10 and f(4)=20. Which of the following is guaranteed by the
Intermediate Value Theorem? Answer: f(x)=13 has at least one solution
in the open interval (2,4)
◉the graph of (e^tanx)-2 crosses the x-axis at one point in the interval
[0,1]. What is the slope of the graph at this point? Answer: 2.961
◉a particle moves along the x axis. the velocity of the particle at time t
is given by v(t), and the acceleration of the particle at time t is given by
a(t). which of the following gives the average velocity of the particle
from t=0 to t=8 Answer: 1/8!v(t)dt from 0 to 8
◉the graph of f' is shown above. which of the following statements must
be true? bell graph Answer: I and III only
◉water is pumped into a tank at a rate of r(t)=30(1-e^-.16t) gallons per
minute. if the tank contained 800 gallons of water when the pump was
turned on, how much water to the nearest gallon is in the tank after 20
minutes? Answer: 1220 gallons
, ◉if f'= the square root of (x^4+1)+x^3-3x, then f has a local maximum
at x= Answer: .350
◉the graph above gives the velocity in ft/sec of a car for 0<t<8, where t
is the time in seconds. Of the following, which is the best estimate of the
distance traveled by the car from t=0 until the car comes to a complete
stop? Answer: 210ft
◉for -1.5<x<1.5, let f be a function with first derivative given by f'x=
e^(x^(4)-2x^(2)+1)-2. Which of the following are all intervals on which
the graph of f is concave down? Answer: (-1.5,-1) and (0,1)
◉the graph f' is shown in the figure above. the function f has a local
maximum at x=?mountain looking graph crosses the x axis at x=1
Answer: -3
◉if f'>0 for all real numbers x and the integral from 4 to 7
f(t)dt=0, which of the following could be a table of values for the
function f? Answer: x f(x)
4 -4
5 -2
75
WITH COMPREHENSIVE MATHEMATICS
QUESTIONS
◉let f b a function that is continuous on the closed interval [2,4] with
f(2)=10 and f(4)=20. Which of the following is guaranteed by the
Intermediate Value Theorem? Answer: f(x)=13 has at least one solution
in the open interval (2,4)
◉the graph of (e^tanx)-2 crosses the x-axis at one point in the interval
[0,1]. What is the slope of the graph at this point? Answer: 2.961
◉a particle moves along the x axis. the velocity of the particle at time t
is given by v(t), and the acceleration of the particle at time t is given by
a(t). which of the following gives the average velocity of the particle
from t=0 to t=8 Answer: 1/8!v(t)dt from 0 to 8
◉the graph of f' is shown above. which of the following statements must
be true? bell graph Answer: I and III only
◉water is pumped into a tank at a rate of r(t)=30(1-e^-.16t) gallons per
minute. if the tank contained 800 gallons of water when the pump was
turned on, how much water to the nearest gallon is in the tank after 20
minutes? Answer: 1220 gallons
, ◉if f'= the square root of (x^4+1)+x^3-3x, then f has a local maximum
at x= Answer: .350
◉the graph above gives the velocity in ft/sec of a car for 0<t<8, where t
is the time in seconds. Of the following, which is the best estimate of the
distance traveled by the car from t=0 until the car comes to a complete
stop? Answer: 210ft
◉for -1.5<x<1.5, let f be a function with first derivative given by f'x=
e^(x^(4)-2x^(2)+1)-2. Which of the following are all intervals on which
the graph of f is concave down? Answer: (-1.5,-1) and (0,1)
◉the graph f' is shown in the figure above. the function f has a local
maximum at x=?mountain looking graph crosses the x axis at x=1
Answer: -3
◉if f'>0 for all real numbers x and the integral from 4 to 7
f(t)dt=0, which of the following could be a table of values for the
function f? Answer: x f(x)
4 -4
5 -2
75
