1yes bhaiya.... ans comes out 2 be P/4.....mine too.... bt its given p/2!!!!
1) What must the radius of a circle be for the sector whose perimeter is equal to the given number P to have the greatest possible area?
(my ans doesn't match)
2) Which of the cylinders with the given perimeter P=100cm, of the axial section has the greatest possible area of the lateral surface?
(plz xplain wat axial section exactly means)
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8 Answers
621st one is very simple..
it is given that 2R+θR=P
maximize θ/2 R2
SO same as maximizing (P-2R)R.2
Now solve
111) Which of these are infinitely large??
a) y=2x sin-1(sinx) as x-->+∞
b) y=(2+sinx)logx as x-->+∞
c) y=(1+sinx) logx as x-->+∞
2) Prove that if the limit of the function f(x) is equal to 'a' as x-->∞, then f(x) is representable as sum f(x) = a+g(x), where g(x) is is an infinitesimal as x-->∞.
3)The function un takes on the following values
u1=1/4; u2=1/4 + 1/10;...... un=1/(3+1) + 1/(32+1) +.......+ 1/(3n+1)....
Prove that un tends to a certain limit as n-->∞
4) Prove the theorem - if the difference between two functions for one and the same variation of the independent variable is an infinitesimal, one of them increasing, the other decreasing at the same time, then both the functions tend to one and the same limit.
5) How many points of discontinuity (and of what kind) has the function y=1/log!x! ?? (!x!=mod x)
23euclid , for 2nd i m not sure if it is correct
consider f(x) - g(x) .
Let this be equal to some k
so f(x) = g(x) + k
so g(x) = f(x) - k
now lim g(x) = 0
x->∞
so lim [ f(x) - k ] = 0
x->∞
so lim f(x) = k
x-> ∞
hence a = k
1but qwerty hw did u get lim(x-->∞) g(x)=0 ??
that means the question is true for any tending value of x???
106oops yes.. i din see that it was 1+sinx
as sinx can be anything between -1 and 1, for x-->∞, sinx can be -1 also so, 1+sinx = 0 (exact) (for some values of x)
so its only (b) as 2+sinx can never be equal to zero
similarly it wont be (a) cuz sin-1(sinx) can be zero also