IIT JEE , AIEEE Forum - Articles Category , Community shelf - BEAT THE TIME TRAPS--SHORTCUT TECHNIQUES ...IN CHAPTER LIMITZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ

beethoven

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)

2.

_x

₀ (sin ax

sin bx)/(sin cx

sin dx ) = (a

b)/(c

d) {also applicable in tan case also)

3.

_x

_a (x^p- a^p)/(x^q-a^q) = (p/q)a^p-q

4.

_x

₀ {^p

(a+xⁿ)- ^p

(a-xⁿ) } / (xⁿ) = 2a^{1/p -1}/p

5.

_x

₀^p

(a+xⁿ) - ^p

a / xⁿ = a^{1/p - 1}/ p

6.

_{[ x]}

(xⁿ+yⁿ)^1/n =y , where o<x<y

7.

_{[ x]}

(1^p+2^p...........+n^p)/n^p+1= 1/(p+1)

8.

_{[ x]}

(x²+ax+b)^x+e/ (x²+cx+ d )^x+e = e^a-c

9.

_{[ x]}

(x²+ax+b)^px+e/ (x²+cx+d)^px+e = e^p(a-c)

10.

_{[ x]}

_af(x)^g(x) =e*_{[x ]}

_{[a ]} g(x)( f(x)-1)

if u have found this article useful plz comment and rate it