CALCULUS FINAL EXAM fully solved &
2026/2027 updated
evaluate the integral 2/1, ln(x)/x dx - answer-(ln2)^2/2
consider the function f(x)=x^4-4x^3. which of the following is NOT
true - answer-f has a local extrema at x=0 and x=3
find the work done by a force F=sqroot 2x+1 N to move an object
along a straight path from a distance of 0 meters to a distance of 4
meters - answer-26/3 J
an object is moving along the x-axis. Let s(t), v(t) and a(t) be functions
giving the position, the velocity, and the acceleration of the object at
time t. which of the following statements is correct? - answer-the
speed of the object at time t is given by s'(t)
stretch the graph of f(x)=x^2 vertically by a factor of 2 and reflect it
about the y axis. what function do you get? - answer-g(x)=2x^2
which statement is correct about the function f(x)=(x+1)/sqroot
x^2+1? - answer-f has two horizontal asymptotes
suppose you charge $45/hour to tutor calculus and you work 10
hours a week. by raising your hourly rate you would lose business at
a rate of 1 hour per $3 increase. Which expression below would you
use to optimize your income using calculus? here x stands for the
,CALCULUS FINAL EXAM fully solved &
2026/2027 updated
number of dollars that the tutor increases the hourly rate - answer-
(45+x)(10-x/3)
find the absolute extrema of f(x)=(x^4/4)-2sqrootx on the interval
[0,4] - answer-absolute minimum: -7/4 absolute maximum: 60
on the graph of the function f(x)=(1+x)^2 which of the following
represents the slope of the tangent line to the graph at the point
with x-coordinate 1? - answer-lim h->0 (1+h)^2-4/h
which of the following integrals computes the area of the region that
lies above the parabola y=(x-2)^2 and below the line y=x? - answer-
integral 4/1, (-x^2+5x-4)dx
P(x, sqroot5/3) is a point on the unit circle in the second quadrant,
and theta is the angle whose terminal side passes through P. find the
value of tan theta. - answer--sqroot5/2
how many solutions does the equation sin(x)=-sqroot3/2 have on the
interval [0, pi]? - answer-None
shift the graph of f(x)=3sqrootx by one unit upward and two units to
the right. what function do you get? - answer-g(x)=3sqrootx-2+1
, CALCULUS FINAL EXAM fully solved &
2026/2027 updated
consider the function y=f(x). below is a table of values for the
function f. based on this table only, what is the best estimate for the
limit lim x->1 f(x) - answer-lim x->1 f(x) does not exist
if lim x->3 f(x)=2, lim x->4 f(x)=-5, lim x->3 g(x)=-1, and lim x->4
g(x)=4, then the limit lim x->4 (2f(x)-3g(x)+4) is equal to - answer--18
if s(t) represents the position of an object at time t, then lim t->1 s(t)-
s(1)/t-1 represents - answer-the instantaneous velocity of the object
at time t=1
the linear approximation of f(x)=sec(x) at a=pi/3 is - answer-L(x)=2
sqroot 3x+2-2pi/sqroot 3
which of the following statements is FALSE about f(x)=e^x - answer-
the range of f is (-inf, inf)
which of the following statements is true about a function f defined
on a closed and bounded interval [a, b]? - answer-if f is continuous,
then f has both an absolute maximum and an absolute minimum on
[a. b]
2026/2027 updated
evaluate the integral 2/1, ln(x)/x dx - answer-(ln2)^2/2
consider the function f(x)=x^4-4x^3. which of the following is NOT
true - answer-f has a local extrema at x=0 and x=3
find the work done by a force F=sqroot 2x+1 N to move an object
along a straight path from a distance of 0 meters to a distance of 4
meters - answer-26/3 J
an object is moving along the x-axis. Let s(t), v(t) and a(t) be functions
giving the position, the velocity, and the acceleration of the object at
time t. which of the following statements is correct? - answer-the
speed of the object at time t is given by s'(t)
stretch the graph of f(x)=x^2 vertically by a factor of 2 and reflect it
about the y axis. what function do you get? - answer-g(x)=2x^2
which statement is correct about the function f(x)=(x+1)/sqroot
x^2+1? - answer-f has two horizontal asymptotes
suppose you charge $45/hour to tutor calculus and you work 10
hours a week. by raising your hourly rate you would lose business at
a rate of 1 hour per $3 increase. Which expression below would you
use to optimize your income using calculus? here x stands for the
,CALCULUS FINAL EXAM fully solved &
2026/2027 updated
number of dollars that the tutor increases the hourly rate - answer-
(45+x)(10-x/3)
find the absolute extrema of f(x)=(x^4/4)-2sqrootx on the interval
[0,4] - answer-absolute minimum: -7/4 absolute maximum: 60
on the graph of the function f(x)=(1+x)^2 which of the following
represents the slope of the tangent line to the graph at the point
with x-coordinate 1? - answer-lim h->0 (1+h)^2-4/h
which of the following integrals computes the area of the region that
lies above the parabola y=(x-2)^2 and below the line y=x? - answer-
integral 4/1, (-x^2+5x-4)dx
P(x, sqroot5/3) is a point on the unit circle in the second quadrant,
and theta is the angle whose terminal side passes through P. find the
value of tan theta. - answer--sqroot5/2
how many solutions does the equation sin(x)=-sqroot3/2 have on the
interval [0, pi]? - answer-None
shift the graph of f(x)=3sqrootx by one unit upward and two units to
the right. what function do you get? - answer-g(x)=3sqrootx-2+1
, CALCULUS FINAL EXAM fully solved &
2026/2027 updated
consider the function y=f(x). below is a table of values for the
function f. based on this table only, what is the best estimate for the
limit lim x->1 f(x) - answer-lim x->1 f(x) does not exist
if lim x->3 f(x)=2, lim x->4 f(x)=-5, lim x->3 g(x)=-1, and lim x->4
g(x)=4, then the limit lim x->4 (2f(x)-3g(x)+4) is equal to - answer--18
if s(t) represents the position of an object at time t, then lim t->1 s(t)-
s(1)/t-1 represents - answer-the instantaneous velocity of the object
at time t=1
the linear approximation of f(x)=sec(x) at a=pi/3 is - answer-L(x)=2
sqroot 3x+2-2pi/sqroot 3
which of the following statements is FALSE about f(x)=e^x - answer-
the range of f is (-inf, inf)
which of the following statements is true about a function f defined
on a closed and bounded interval [a, b]? - answer-if f is continuous,
then f has both an absolute maximum and an absolute minimum on
[a. b]
