limit

JEE Main Preparation › Calculus questions › limit

Q1. find the limit
lim(xâ†’0) (1+x)^{^1/x}-e+(ex/2)x²

Q2. Let the rth term t_{_r} of a series be given by t_r = r1+r²+r⁴. Then find the value of lim(nâ†’âˆž) Î£t_r (n=1 to n=n)

Q3. If x is a real number in [0,1]. Then the value of lim lim [1+cos^2m(n!Î x)]
^{(mâ†’âˆž)}^{(nâ†’âˆž)}

#Mathematics #Calculus

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5 Answers

11

Mani Pal Singh ·2009-07-31 03:29:15

Q1 lagao expansions or
u know that (1+x)^1/x=e when limit x->0
u got ex/2x²
now check the question
something missing

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106

Asish Mahapatra ·2009-07-31 03:33:03

actually the Question says 2 prove that the limit is 11e/24
par mera aa rahaa tha lim does not exist..

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11

Mani Pal Singh ·2009-07-31 03:36:31

have u tried expansions

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66

kaymant ·2009-07-31 06:06:14

2) Transform t_r as
t_r = 12 . 2r(r² + r +1)(r² - r + 1) = 12 . (r² + r +1) - (r² - r + 1)(r² + r +1)(r² - r + 1)
=12 (1r² - r + 1 - 1r² + r + 1 )

Now the sum telescopes to give

S_n = 12 (1 - 1n² + n + 1 )

So as n â†’ âˆž, S_n â†’ 12

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24

eureka123 ·2009-07-31 06:29:06

Q3 is very standard...
it was solved by nishant sir here..
http://targetiit.com/iit-jee-forum/posts/area-262.html?dpid=1522[1]

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Basic Integral Calculus Operators Symbols Matrix Cases

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