By A. Ganesh (Author), Balasubramanian G. (Author)
Read Online or Download Engineering Mathematics- II (As per the new syllabus of VTU (B. E. , II Semester) PDF
Best engineering books
New PDF release: The Works: Anatomy of a City
How a lot do you actually find out about the structures that maintain a urban alive? The Works: Anatomy of a urban includes every little thing you ever desired to find out about what makes ny urban run. for those who flick in your mild change the sunshine is going on--how? in case you placed out your rubbish, the place does it move? for those who flush your rest room, what occurs to the waste?
Download PDF by Ion Boldea, Syed A. Nasar: The induction machine handbook
Known as the workhorse of undefined, the arrival of strength electronics and advances in electronic keep watch over are remodeling the induction motor into the racehorse of commercial movement regulate. Now, the vintage texts on induction machines are approximately 3 many years previous, whereas newer books on electrical cars lack the required intensity and element on induction machines.
In contrast to conventional computing, Computational Intelligence is tolerant of vague details, partial fact and uncertainty. This publication offers a particular choice of contributions on a centred remedy of significant components of CI, concentrated on its key aspect: studying. the entire individuals of this quantity have direct bearing with this factor.
- Fundamentals of Gas Dynamics
- Newnes Engineering Materials Pocket Book
- Whitewares and Materials: Ceramic Engineering and Science Proceedings, Volume 24, Issue 2
- Knowlege-Based and Intelligent Information and Engineering Systems: 15th International Conference, KES 2011, Kaiserslautern, Germany, September 12-14, 2011, Proceedings, Part II
- Air Pollution. Volume VII: Supplement to Measurements, Monitoring, Surveillance, and Engineering Control
- IAENG Transactions on Engineering Sciences: Special Issue of the International MultiConference of Engineers and Computer Scientists 2013 and World Congress on Engineering 2013
Additional resources for Engineering Mathematics- II (As per the new syllabus of VTU (B. E. , II Semester)
Example text
2 ar OP a (vi) r = b1 − cos θg 3 PQ 2 MN LM Ans. na OP (viii) r = a sin nθ N 2Q n rn an n −1 3. If ρ1 and ρ2 are the radii of curvature at the extremities of any chord of the cardiode 2 2 r = a (1 + cos θ) which passes through the pole. 1 Rolle’s Theorem If a function f (x) is 1. continuous in a closed interval [a, b], 2. differentiable in the open interval (a, b) and 3. f (a) = f (b). Then there exists at least one value c of x in (a, b) such that f ′ (c) = 0 (No proof). 2 Lagrange’s Mean Value Theorem Suppose a function f (x) satisfies the following two conditions.
F (x) is differentiable in the open interval (a, b). Then there exists at least one value c of x in the open interval (a, b), such that bg f (b) – f a b–a = f ′ (c) 28 ENGINEERING MATHEMATICS—II Proof. (1) where k is a constant. Since f (x), kx and φ (x) is continuous in [a, b], differentiable in (a, b). (2) Hence, if k is chosen as given by (2), then φ (x) satisfy all the conditions of Rolle’s theorem. Therefore, by Rolle’s theorem there exists at least one point c in (a, b) such that φ′(c) = 0.
7. Prove that b–a 1 – a2 < sin–1 b – sin–1 a < b–a 1 – b2 where a < b < 1. (3) 1 – b2 Combining (2) and (3), we get 1 1– a 2 1 or 1 – a2 1 < 1– c < 2 < 1 1 – b2 sin –1 b – sin –1 a < b–a 1 1 – b2 On multiplying by (b – a) which is positive, we have b–a 1– a 2 < sin–1 b – sin–1 a < b–a 1 – b2 by using (1) 39 DIFFERENTIAL CALCULUS—I 8. Show that b–a b–a π 3 4 π 1 –1 –1 , if 0 < a < b and deduce that + < tan –1 < + · 2 < tan b – tan a < 1 + a2 1–b 4 25 3 4 6 Solution Let f (x) = tan–1 x is continuous in [a, b], a > 0.
