158 - Mathematics Questions Answers

If a,b and c are positive real numbers, show that

ab+c+bc+a+ca+b32

Asked By: MROY
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Joshi sir comment
How to do it without using cauchy schwartz inequality?
Asked By: LUFFY
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Asked By: LUFFY
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Joshi sir comment

Let the lines in the pair are m1x-y=0 and m2x-y=0 Find perpendiculars from (x,,y,) on lines and calculate their sum Use formulae m1+m2 = -2hb and m1m2= ab Inform for any issue

 

How to do it with calculus?
Asked By: LUFFY
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Joshi sir comment

length for one turn = 3

Draw diagonal of a rectangle then turn it as a cylinder, you will get the construction given in the question.

In triangle l = 32+n2 So total length of wire having n turn = n32+n2 Compare with 20 and solve

 

Can it be solved by finding area ?
Asked By: LUFFY
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Joshi sir comment
Sir pls solve
Asked By: KANDUKURI ASHISH
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Joshi sir comment

The general solution of this kind of  differential eq. is y = eax Let a function g(x) = eaxf(x)    (1) differentiate eq. (1) thrice for getting g,,,(x) now for getting the same function as given  find a. you get the same function for  a = 1/2. clearly, for min 5 zeros of g(x), there are min 2 zeros for g,,,(x).  solve and inform if face any problem.

Plzz help me to solve this question ☺️☺️☺️
Asked By: ASHLOK
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Joshi sir comment

Find 

lim n→∞  ⁿ√(n!) / n

Asked By: LUFFY
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Is there a way to do this in terms of area in a coordinate plane. Where difference of larger and smaller can be difference in x coordinate for 1st player and difference in y coordinate for 2nd player
Asked By: LUFFY
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Joshi sir comment

Probability to get following differences  difference     probability 0                   6/36 1                 10/36 2                   8/36 3                   6/36 4                   4/36 5                   2/36 So required probability =1-2636436+236+1036236 now solve problem is based on integral values so area is not very useful

Find Sum to n terms 

 

x/1-x²  +  x²/1-x⁴  +  x⁴/1-x⁸ + ....

Asked By: LUFFY
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Joshi sir comment

x1-x2=11-x-11-x2 break all terms similarly and solve 

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