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In this post we are providing you CS201Quiz-3 Solution Fall 2022 (23 to 33) 100% correct or right solution. You'll Download assignment Solution File From below download (Click Here For Download File) link interface.
Quiz No 3 will be opened from
19th February,2022 to 21th February, 2022.
Arc length of the curve y=x from x =0 to x=2 is
-------.
All of the
above
If the upper and lower limits for the definite
integral are the same, then ∫aaf(x)dx=If the upper and lower limits for the
definite integral are the same, then ∫aaf(x)dx=
Zero
The value of ∫12dx=
1
The volume by the Washers generated by revolving the
region around yaxis is given by the formula ----------
∫abÏ€([u(y)]2+[v(y)]2)dy
.Let R be the plane region bounded above by a
continuous curve y=f(x) below by the x-axis and on the left and right,
respectively, by the lines x=a and x=b the volume of the solid generated by
revolving R about the y-axis is given by ______.
V=∫ab2Ï€xf(x)dx
The method of slicing by integration is used for
finding ----------
Volume
x = 1 to x = 3 is ________.
4
IfF(x)istheanti−derivativeoff(x)on[a,b],i.eF/(t)=f(x),thenIf
F(x)istheanti−derivativeoff(x)on[a,b],i.eF/(t)=f(x),then
∫baf(x)dx=F(b)−F(a)
For a sequence { an} if the difference
between successive terms an+1-an ≥ 0.
None
decreasing
Distance formula is based on the ------.
Pythagoras
theorem
The volume V of a cylinder with base area A and
height h is calculated by ------.
V= A h
Distance between (3,-2) and (4, 0) using the
distance formula is --------.
None of these
Definite integral indicating the arc length of the
curve y=x2 between x=0 and x=2 is -------.
None of
these.
Forms of L ‘Hospital’s rule are ------.
All of the
given/above
A ------- Function is a function that has continuous
derivatives up to some desired order over some domain.
Smooth
Find the area between y=z and y= -z (z- 4).
9/2
To get better approximation to actual area under a
continuous curve over a closed intervals we have to increase -------.
Number of subintervals
The area bounded by
the parabola y2=x, straight line y = 4 and y
axis is-
64/3
Length of the arc y=c from x=0 to x=1 is -------.
1
A strictly monotone sequence is --------.
Increasing or
decreasing
For a sequence {an} if the ration of
successive terms an+1/an ˂ 1 then the sequence is known
as
Decreasing
If {-8, 8} is subdivided into ‘16’ equally
subintervals, the RIGHT end point if 13th sub-intervals will be --------.
4
If y= 3x, then instantaneous rate of change of ‘y’
w.r.t ‘x’ at ‘5’ is --------.
2
Consider the function defined by f(x) = 2/(x-1) the
point of discontinuity is -------.
X=3.
If f(x) = x’ (3/2) then f’ (1)= NOTE: x’n means ‘x’
to the power ‘n’
1
Which of the following point satisfies the equation:
2x + 5y =15?
(5, 1)
What is the derivative of sin (20x)?
20Cos (20x)
What is the derivative of 3sec (x)?
3 Sec(x)
Tan(x)
Which of the following is solution of equation:
|3x+4| = |2x|
Does not
exist
Which of the following is distance between the
points (2, 5) and (-1, 1)?
5
------------- Of domain must have image in the range
under the defined function.
Each element
Arc length of the curve y=7 from x=0 to x=1 is
------.
1
Arc length of the curve y=x from x=0 to x=2 is
------
2√2
If the interval [3, 7] is divided into ‘4’ equal
subintervals, then left endpoint of each subinterval will be --------.
4,5,6,7.
Length of the curve y=3x from x=0 to x=1 is -------.
Sqrt (10)
Length of the curve y=4x from x=0 to x=1 is -------.
Sqrt (17)
Integral of (1-2x) from [0, 1] is -------.
0
. By the use of L’Hopital’s rule the value of
2
-------- gives a relation between definite integral
and indefinite integral.
First
fundamental theorem of calculus
A monotone sequence is either non decreasing or
________.
Non
Increasing
a sequence is a function whose ______ is the set of
positive integers
domain
The length of the WHOLE polygonal path will be
None of these
a plane curve (not line) is a curve that lies in a
_____ plane.
Two
dimensional
The volume of solid obtained when the region under
the curve x=y over the interval [1,4] is revolved about the y-axis is
V=∫14Ï€y2dy
Integral of (1-2x) from [0,1] is ………..
0
The volume of the solid bounded by planes y=a and
y=b with crosssectional area A(y) perpendicular to the y-axis is
V=∫abA(y)dyV=∫abA(y)dy
∫abf(x)dx=______.
−∫baf(x)dx−∫baf(x)dx
EVERY continuous function on an interval has an
anti-derivative ……………
On that
interval
In integration of f(x)=x(x^2 +1)^3 from x=0 to x=2
by substitution method, we take u=x^2+1 then du= ................
2xdx
First fundamental theorem of calculus gives the
definite integral of a .......... function on a given closed interval in a
quick way.
Continuous
x44−14=___
∫1xt3dt
.If the solid is revolved around the y-axis and
generates a solid with a circular cross section of radius g(y) at y. Then the
area of this cross section is
Ï€[g(y)]2Ï€[g(y)]2
If the upper and lower limits for the definite
integral are the same, then ∫aaf(x)dx=If the upper and lower limits for the
definite integral are the same, then ∫aaf(x)dx=
negative
integer
The integral of f(x) =sin(x) from x=0 to x=pi is
0
If f(x) =3x^2 then F(x) (antiderivative of f) will
be
6x
If the upper limit of Definite Integral is equal to
its lower limit, then the value of Definite Integral will be _______.
Zero
The volume of a cylinder is the area of a cross
section of the cylinder multiplied by the ________ of the cylinder.
Height
Find them are a between y=x and y=−x(x−4) Find the area
between y=x and y=−x(x−4)
None of these
Why the equation: x*2 +8=0 does not have approximate
solution while using Newton's method?
x*2 will
atways be nonnegative
If Newton's Method succeeded to get the opproximete
solution of an equotion, then which of the following is NOT true obout it.
The tangent
line (at any approximated point) is not parallel to x-axis.
Summation of 2 where sum ranges from 0 to 10 equals
20.
True
If the closed interval f-10,x] is divided into 20'
equelly spaced subintervels each of which having the width equals to 1' unit
then the value of* is
10
In opproximation to en area Rn (where n is
subscript) when limit is taken as n goes to infinity, approximation becomes
actual erea
False
What are criticel points of the function f(x) =*-1?
x=1
.Let A be the area of a rectangle under a continuous
function f(x) over a closed interval (o, b]. If this area is divided in to 'n'
sub-rectangles then width of each epproximated sub-intervals is –
(b-o)/n
Increase in number of rectangles under anycontinuous
function gives pproximation to erea.
Better
If fx)= Sec* (2) x+x*3, then which of the fallowing
is NOT true about it.
Its anti-derivative is Tanx)+
x^4/4+ 15
Integretion of 5 with respect to x is.
5x
If fx)=x4, then which of the following is Not true
about it.
Its
anti-derivative is x"5/5.
Let y f() be a discontinuous function on a finite
closed interval, then which ofthe following is true about it.
It must have absolute extreme
values
Integrel of 52 is NOTE: X'n meens '* to the power'n
25x
Sum of n-terms of a series whose nth term is 'n'=
1/n*1.then what is the sum ofthe firsttwo terms is
5/6
x=1 is a critical value of the function.
f(x)=(x-1)*3 Tolal Marks: 1 NOTE:xn means 'X to the power'n.
True
Which of the following wil be left end points if the
interval (-2,2] is divided into 4 equal subintervals.
-2,-1,1,2
Why the equation: x^2 +8=0 does not have apprcximete
solution while using Newton's method?
X^2 will at
ways be nonnegative
Ifx= (1^2)(2^2)+(3^2)+(4^2)+... +(302), then x=
9455
Newton's method uses the to approximate the root.
Tangent line
The polynamial function f(x)=6x^2-30x+36 has the
critical point over the reel line is
5/2
If fx)=x^5+6, then which ofthefollowing is Not true
ebout it.
Its anti -
derivative is x^6/6 + 6x+ 6
If x=1+2 +3+4...+20,then x =
210
In sigm nctetion 12+14+16+18+20 can be written as.
summation of
(2k) where (k varies from 6 to10)
If f(x)=Tan(x) then mean value theorem can be
applied to it on the interval (0,2pi)
False
If 'n' goes from 1 to 4 and the summation of 'na'
=Maxima of (e^x) in the interval[-e,0]. then the value of 'a' is
10
Subdivide the interval [o, b] into 4 equal
subintervals then the width of each subinterval is
(b-a)/4
If(x)=x^4, then which af the following is Not true
about it.
Its
anti-derivative is x^5+5.
If 2x+7 is defined on the interval (2,4). then which
of the following is true about it
It has both
absolute maximum and minimum values
The indefinite integrel of 5sinx is
-5cosx+c
If 'n' goes from 1 to 3 and the summation of 'na' =
6, then the value of 'a' is –
Undetermined
1+23+-------+1000 equels
500500
If (x) = |x| -2 is defined as the interval [-2, 2].
then which of the following is true about it.
There is a
point in the interval (-2, 2) where f(x) has a horizontal tangent
Which of the following is the absolute minima of the
function ; f (x) in the interval [-1,1]?
1
If f(x)= Cos(x) + Sin(x)+x, then which of the
following is NOT true about it.
Its anti -
derivative is Sin(x)- Cos(x) + x^2/2+4.
Maximum of the function f(x)=2x^7 occurs at
X=0
Maximum of the function f(x) =2x^7 occurs at
x=-7/2
What are critical points of the function f(x)
=x^2-1? NOTE: X^n means 'x’ to the power 'n’
X=0
summation of(ei) (i varies from 1 to n), summation
of (oj) g varies from 1 to n),summation of (ak) (k varies from 1 to n) All
these three represents same summation
True
Subdivide the interval [3, 5] into n equal parts,
and then the width of each subinterval is
2/n
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