Find the equation of the curve with the given derivative of y with respect to x that
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Find the equation of the curve with the given derivative of y with respect to x that passes through the given point:
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a dydx 3x 2x Integrating both sides wrt x dydx dx dy 3x 2x c c is the constant of integration or y 3x 3 2x 2 c x x c Since the curve passes through P2 10 P satisfies the equation 10 2 2 c or c 10 8 4 2 y x x 2 b dydx 4x 2x 3 Integrating both sides wrt x dydx dx dy 4x dx 2x dx 3 dx c c is the constant of integration or y 4x 4 4 2x 3 dx 3x c x 4 2x 2 2 3x c x 4 x 2 3x c To evaluate c substitute the coordinates of point P1 4 in the obtained equation or 4 1 1 3 c or c 1 y x 4 1 x 3x 1 c dydx x 14 x Integrating both sides wrt x y x dx 14 x dx c c is the constant of integration or y x dx 14 x dx c x 121 121 14 x dx c 23 x 32 14 x 3 c 23 x 32 112 x c As the curve passes through P4 11 therefore P satisfies the equation or 11 23 4 32 112 4 c or c 11 163 163 13 y 23 x 32 112 x 13 d dydx 3x x Integrating both sides wrt x y 3 1 x dx x dx c c is the constant of integration or y 3 ...View the full answer
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Ankit Jangra
Career Summary: Over twenty five years of teaching experience, more than half of which in Engineering subjects and a significant half in MBA entrance level exams. Here is a short gist.
Work Experience: Alumni of a national institute of technology in computer science and an IIM (a prestigious management institute in India and globally) call getter (98.7 percentile).
Had also been a project guide on one occasion for a Engineering final year project in designing a Network Intrusion Detection System, an advanced firewall mechanism that dealt with network security. Have also designed many software projects from games to online payment to network data transfer format and interchange.
Have also written three university level text book notes on C and Data Structure, Digital circuits and Engineering Mathematics.
Had been teaching and mentoring MBA aspirants in reputed institutes of the country.
Associated with an academy for the last seven years teaching subjects like Aptitude, C and Data Structure, Analysis of Algorithm, Operating System, Digital Circuits for post graduate entrance exams and also had the privilege of being a guest lecturer in many government universities across the country.
Computer Literacy: Have detailed and intricate and extensive knowledge of Core Java, Enterprise Java, React, Spring Framework, Hibernate, LDAP (server directory structure) and Scala Actor System and Databases like MySql, Mongodb, PostgreSql. Teaching Java fundamentals from basic to advanced, from Java Memory model to Reference objects, to UTC Date Time format, to responsive Java, to design patterns, to JUnit test, to ForkJoin thread pool, only a few samples to count. Only recently, (for academic interest) designed a Json converter (Json to Java object and vice versa) from scratch like Jackson, for mongoDB application. Also designing web applications both front and backend, with knowledge of React, HTML, CSS, Javascript. Have been teaching Java for more than seven years.
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Related Book For 
Edexcel AS And A Level Mathematics Pure Mathematics Year 1/AS
ISBN: 9781292183398
1st Edition
Authors: Greg Attwood
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