# 135 - Mathematics Questions Answers

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.

Joshi sir comment
Joshi sir comment

Joshi sir comment

Find

lim n→∞  ⁿ√(n!) / n

Joshi sir comment 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
Joshi sir comment

Find Sum to n terms

x/1-x²  +  x²/1-x⁴  +  x⁴/1-x⁸ + ....

Joshi sir comment

1 . Iₙ = ∫ ( 1/ ( x² + a²)ⁿ  )dx

How to do this by substituting x = a tan Α

2.  Is this true

∫ f(x) d(kg(x)) = k ∫ f(x) d(g(x))

where k is a constant

Solution by Joshi sir

d/dx((1+x^2+x^4)/(1+x+x^2))=ax+b

then a=?, b=?

Joshi sir comment

1+x2+x4 = (1+x+x2)(1-x+x2)

now solve

Maths >> Calculus >> Functions IIT JEE

Find a formula for a function g(x) satisfying the following conditions

a) domain of g is (-∞ , ∞ )     b) range of g is [-2 , 8]     c)  g has a period π   d)  g(2) = 3