Vriti EdustoreMATHEMATICS - FEW FORMULAE IN LIMITS
13 Jul 2011 23:12:39 IST
MATHEMATICS - FEW FORMULAE IN LIMITS
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Limits
COURTESY: MTG MATHEMATICS TODAY..........
HERE ARE SOME TRICKS WHICH ARE VERY USEFUL IN EVALUATION OF LIMITS FOR COMPETETIVE EXAMS...
1.
X
0 (Sin mx)/(Sin nx) = m/n (also applicable when tan is present in place of sin)
0 (Sin mx)/(Sin nx) = m/n (also applicable when tan is present in place of sin)2.
x0 (sin ax 
sin bx)/(sin cx sin dx ) = (ab)/(cd) {also applicable in tan case also)
0 (sin ax sin bx)/(sin cx sin dx ) = (ab)/(cd) {also applicable in tan case also)3.
xa (xp- ap)/(xq-aq) = (p/q)ap-q
a (xp- ap)/(xq-aq) = (p/q)ap-q4.
x0 { p
(a+xn)- p(a-xn) } / (xn) = 2a1/p -1/p
0 { p(a+xn)- p(a-xn) } / (xn) = 2a1/p -1/p5.
x0 p (a+xn) - pa / xn = a1/p - 1 / p
0 p (a+xn) - pa / xn = a1/p - 1 / p6.
[ x]
(xn+yn)1/n =y , where o<x<y
(xn+yn)1/n =y , where o<x<y7.
[ x] (1p+2p...........+np)/np+1 = 1/(p+1)
(1p+2p...........+np)/np+1 = 1/(p+1)8.
[ x] (x2+ax+b)x+e / (x2+cx+ d )x+e = ea-c
(x2+ax+b)x+e / (x2+cx+ d )x+e = ea-c9.
[ x] (x2+ax+b)px+e/ (x2+cx+d)px+e = ep(a-c)
(x2+ax+b)px+e/ (x2+cx+d)px+e = ep(a-c)10.
[ x]a f(x)g(x) =e*[x ][a ] g(x)( f(x)-1)
a f(x)g(x) =e*[x ][a ] g(x)( f(x)-1) if u have found this article useful plz comment and rate it
Comments (6)
anup
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Joined: 24 Dec 2011 16:30:07 IST
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24 Dec 2011 16:30:08 IST
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mst h
12 May 2013 17:41:21 IST
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joint prepatn,enginnering notes,ebooks,gates books,ies books, and many more exam books and notes and papers,iit prepatn, come to http://vtuforall.blogspot.com/2013/05/blog-post_8178.html
12 May 2013 19:27:42 IST
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Gr888But, in point 10,formula is applicable,if f(x)-> 1 and g(x)-> infinity only.
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