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CBSE Class 12-science Answered

Find the equation of the normal to the curve y = 2x2 + 3 sin x at x = 0.
Asked by Topperlearning User | 07 Aug, 2014, 12:49: PM
answered-by-expert Expert Answer

The equation of the given curve is

y = 2x2 + 3 sin x           …(i)
Putting x = 0 in (i), we get y = 0
So, the point of contact is (0, 0).
Now,
straight y equals 2 straight x squared plus 3 rightwards double arrow open parentheses dy over dx close parentheses equals 4 x plus 3 space cos space x rightwards double arrow open parentheses dy over dx close parentheses subscript left parenthesis 0 comma 0 right parenthesis end subscript equals 4 cross times 0 plus 3 cross times cos space 0 to the power of straight o equals 3
So, the equation of the normal at (0, 0) is
 

straight y minus 0 equals minus 1 third left parenthesis straight x minus 0 right parenthesis space open square brackets using : space straight y minus straight y subscript 1 equals minus 1 over open parentheses dy over dx close parentheses subscript left parenthesis straight x subscript blank comma straight y subscript 1 right parenthesis end subscript left parenthesis straight x minus straight x subscript 1 right parenthesis close square brackets rightwards double arrow straight x plus 3 straight y equals 0

 
Answered by | 07 Aug, 2014, 02:49: PM

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