This document contains a 7 page exam for the course CS-601: Differential and Integral Calculus with Applications. The exam contains 8 questions testing a variety of calculus concepts:
1) Part a contains 6 multiple choice questions testing derivatives, integrals, limits, and monotonicity. Part b contains 6 fill in the blank questions testing derivatives, integrals, and equations of tangents.
2) Questions 2-5 contain additional multiple choice or short answer problems testing continuity, derivatives, integrals, Rolle's theorem, and partial derivatives.
3) Questions 6-8 contain free response problems on geometry, differential equations, and approximating an area using Simpson's rule. The exam tests a comprehensive understanding of
We define the definite integral as a limit of Riemann sums, compute some approximations, then investigate the basic additive and comparative properties
The second Fundamental Theorem of Calculus makes calculating definite integrals a problem of antidifferentiation!
(the slideshow has extra examples based on what happened in class)
We define the definite integral as a limit of Riemann sums, compute some approximations, then investigate the basic additive and comparative properties
The second Fundamental Theorem of Calculus makes calculating definite integrals a problem of antidifferentiation!
(the slideshow has extra examples based on what happened in class)
Elliptic Curve Cryptography and Zero Knowledge ProofArunanand Ta
Elliptic Curve Cryptography and Zero Knowledge Proof
Presentation by Nimish Joseph, at College of Engineering Cherthala, Kerala, India, during Faculty Development Program, on 06-Nov-2013
Elliptic Curve Cryptography and Zero Knowledge ProofArunanand Ta
Elliptic Curve Cryptography and Zero Knowledge Proof
Presentation by Nimish Joseph, at College of Engineering Cherthala, Kerala, India, during Faculty Development Program, on 06-Nov-2013
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2004. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
JMeter webinar - integration with InfluxDB and GrafanaRTTS
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In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
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https://www.rttsweb.com/jmeter-integration-webinar
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Leading Change strategies and insights for effective change management pdf 1.pdf
Cs 601
1. No. of Printed Pages : 7 CS-601
BACHELOR IN COMPUTER
-7r
00
APPLICATIONS
O Term-End Examination
O
June, 2011
CS-601 : DIFFERENTIAL AND INTEGRAL
CALCULUS WITH APPLICATIONS
Time : 2 hours Maximum Marks : 75
Note : Question no. 1 is compulsory. Attempt any three more
questions from question No. 2 to 6. Use of calculator is
permitted.
1. (a) Select the correct answer from the four given 6
alternatives for each part given below :
x2 —1
(i) If f (x) — , then domain of the
x+1
function is :
(A) R, the set of real numbers.
(B) —1, ]
(C) All real numbers except - 1
(D) none of these
CS-601 1 P.T.O.
2. (ii) If y = x tan -1 x, then dY -
dx
2
X
(A) x2 tan-ix + II
V1+x2
x
(B) tan-1 x+ 2
1+x
x
(C) tan-1 x- 1+x 2
(D) (tan - 1x)2.
d ex
(iii) —) =
dx x
ex ex 1
(A) (B) - + - ex
2
-
x
1 x ex
(C) - e ---y (D) ex log x
x
(iv) Jcosec (3x + 4) cot (3x + 4) dx =
1
(A) 2 cosec (3x +4) cot (3x +4) + C
1
(B) - cosec (3x + 4) + C
3
_1
(C) cosec (3x +4) + C
(D) log cos (3x + 4) C
CS-601 2
3. (v) If f (x) = (x —1) ex +1 and x 3 0 then
f(x) is :
(A) increasing function
(B) decreasing function
(C) Strictly increasing function
(D) Strictly decreasing function
Lim sin 4x
(vi) x is :
x
(A) 0 (B) 00
(C) 1 (D) 4
(b) Fill in the blanks :
(i) f dx
0 NI -
Lim x 2
x -4 0 sin X2
x
(iii) . 2 sin 2 cos — dx =
1 —
2
(iv) The minimum value of the function
f (x)= (2x —1)2 +3 is
dy
(v) If y = cos x2, then =
dx
(vi) The equation of the normal to the
curve y=x3 at (1, 1) is
CS-601 3 P.T.O.
4. (c) For each of the following functions, find 2
whether the function is monotonically
increasing or monotonically decreasing or
neither, on given interval.
(i) f (x) = 2x3 — 8 on [0, 3]
f (x) = 2 sin x on [0,
2
(d) If x= tan (in y), prove that 4
(1 + x2) yi =y.
Using Leibnitz theorem, find yn +1.
(e) The perimeter of a rectangle is 100 m. Find 3
the length of its sides when the area is
maximum.
(f) Find the value of 'b' for which the function 3
{
x 2+1 when x < 2
f (x) 2
bx+- when x 2
x
is continuous at x= 2.
(g) Evaluate ; 3
3
(logx3+9sin3 x) [27 sin2x cosx+ — ] dx
Lim 11x2 — 6x+8
(h) Evaluate 3
-- 9x2 —5x+5
>04
CS-601 4
5. 2. (a) For what value of k is the function ; 3+4+4+4
2x+1 , x 5_ 2
f (x) Ix+k , x > 2
is continuous at x = 2
dy
(b) Find — if y= sin x sin 2x sin 3x
dx
(c) Evaluate ; fx3 log 2x dx
r _ V x
cos
(d) Prove that dx = —
c;;X
Vsin x+ fc- 4
3. (a) Find the nth derivative of the following
function f (x) = ( ax + b)m where a and b
are real numbers and m is a positive integer.
(b) Can Rolle's Theorem be applied to the
following function ? 5+5+5
y = sin2x on the interval [0, 14 Find
'C' such that f' (C) = 0, in case Rolle's
theorem can be applied.
(c) Integrate any one of the following :
(x3 e2x dx
r1
(ii) dx
e +1
CS-601 5 P.T.O.
6. 4
4. 2x
(a) Evaluate f e dx 5+5+5
0
(b) Compute the area lying between the
parabola y =4x — x2 and the line y = x.
(c) If z = eax + by f (ax — by), prove that
az az
b — +a — = 2 abz
ax ay
5. (a) Solve any one of the following : 5+5+5
dy
(i) xy— =1+x+y+xy
dx
dy X
2
+y 2
(u) — =
dx xy
(b) For what value of 'k' is the following
function continuous at x=1 ?
X 2 -1 X#1
f (x) = {x -1 '
k x =1
(c) If u =f (x—y, y — z, z— x), prove that
au+ + =0
au au
ax ay az
CS-601 6
7. 6. (a) Calculate the radius and the height of a right
circular cylinder of maximum volume which
can be cut from a sphere of radius R.
(b) Solve any one of the following : 5+5+5
(i) dY - e2x -3Y + 4x2 e - 3Y
dx -
(ii) (xy + x) dy - (xy + y) dx = 0
(c) A river is 80 ft wide. The depth in feet at a
distance x ft, from one bank is given by the
following table
x : 0 10 20 30 40 50 60 70 80
d: 0 4 7 9 12 15 14 8 3
1
Using Simpson's 3rd rule, find
approximately the area of the cross-section.
CS-601 7