CALCULUS FINAL EXAM QUESTIONS WITH VERIFIED ANSWERS

CALCULUS FINAL EXAM QUESTIONS
WITH VERIFIED ANSWERS
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

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]

let f be a continuous function which is differentiable at c. which of the following
statements is correct? - ANSWER-f'(c)= f(c+h)-f(c)/h for small h

which of the following statements is true? - ANSWER-integral x/0, sqroot t^3+1 dt is an
antiderivative of sqroot x^3+1

if g(x)= x^4f(x)/1+3x, then which of the following is equal to g'(x)? - ANSWER-g'(x)=
(1+3x)(x^4f'(x)+4x^3f(x))-3x^4f(x)/(1+3x)^2

which of the following is equal to ln (sqroot xy^2/z^3)? - ANSWER-1/2(lnx+2lny-3lnz)

consider the piecewise function
f(x)= x^2+2x-1 if x<0
f(x)=x-1 if x>_0

, which of the following statements is correct about the function f? - ANSWER-the
function f is continuous at x=0 because the left limit limx->0^- and right limit exist and
are the same and equal to f(0)

for which of the following limits is L'Hospital's Rule not applicable? - ANSWER-lim theta-
>0 cos(theta)/theta

suppose the second derivative of f is given to us in factored form by the following
formula: f"(x)=x^4(x+1)^2(x-1)^2. how many inflection points does f have (where f"(x)
changes sign, above x axis is pos, below neg - ANSWER-None

the domain of the function f(x)= |x+5|-2/sqroot x-3 is - ANSWER-(3, inf)

given the graph y=f(x) below, which of the following quantities is the largest? -
ANSWER-integral 4/0, f(x)dx

let f be a continuous function such that f(3.2)=3 and f'(3)=5. which of the following
statements is correct? - ANSWER-f(3) is approx 2

sin^-1(1/2)= pi/6 - ANSWER-

if the position of an object is given by s(t)-2-t^2, then what is the average velocity of the
object over the time interval 1<_t<_3? - ANSWER--4

evaluate the limit lim x->pi (1+tan(x)/(1-cos(x) and explain how to find it - ANSWER-the
limit equals 1/2 and can be found using direct substitution of x=pi into the function

consider the function f(x)= sqroot 17 pi+x^2-33x-19. what is the smallest number n such
that f^n(x)=0 for all x? f^n is the nth derivative of f - ANSWER-3

what expression estimates the integral 4/2, ln xdx using riemann sum with 4 rectangles
and right endpoints? - ANSWER-1/2(ln(2.5)+ln(3)+ln(3.5)+ln(4))

if v(t) represents the velocity of an object at time t, then lim t->1 v(t)-v(1)/t-1 represents -
ANSWER-the instantaneous acceleration of the object at time t =1

find the absolute extrema of f(x)= x^2/4-sqroot x on the interval [0,4] - ANSWER-ab
minimum: -3/4, ab maximum: 2

let f be a function and let c be a value inside the domain of f. which of the following
statements is correct? - ANSWER-f'(c), if exists, measures the instantaneous rate of
change of f at x=c

an object is moving along the x-axis. let s(t), v(t), and a(t) be functions giving the
position, velocity, and acceleration of the object at time t. which of the following
statements is correct - ANSWER-a(t)= s"(t)