Joshi sir comment
Joshi sir comment

Joshi sir comment

Find

lim n→∞  ⁿ√(n!) / n

Joshi sir comment
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

Joshi sir comment

g(x) = 3-5sin(2x-4)

Maths >> Calculus >> Functions IIT JEE

Let f(x) = x135 + x125 - x115 + x5 +1. If f(x) is divided by x3-x then the remainder is some function of x say g(x). Find the value of g(10)

Joshi sir comment

for getting reminder put x3= x so

x135 + x125 - x115 + x5 +1 will give

x45 + x41*x2 - x38*x +x*x2 +1

x15 + x13*x2*x2 - x12*x2*x +x*x2 +1

x17 + x3 +1

x5*x2 + x + 1

x+ x + 1

x2*x + x +1

x3 + x +1

x+x+1

2x+1

now put x = 10