43 - Calculus Questions Answers

Find 

lim n→∞  ⁿ√(n!) / n

Asked By: LUFFY
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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

 

Asked By: LUFFY
is this question helpfull: 2 0 submit your answer
Solution by Joshi sir

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

then a=?, b=?

Asked By: RAJIV
is this question helpfull: 21 9 read solutions ( 2 ) | submit your answer
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

Asked By: VAIBHAV GUPTA
is this question helpfull: 6 0 read solutions ( 1 ) | submit your answer
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)

Asked By: VAIBHAV GUPTA
is this question helpfull: 7 6 submit your answer
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

How to inegrate ( In t) dt /(t-1)

Asked By: PARTHASARATHY
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Joshi sir comment

let lnt = x so dt/t = dx so dt = tdx = exdx

now ∫(ln t)dt/(t-1) = ∫xexdx/(ex-1) = ∫x(ex-1+1)dx/(ex-1)

now solve 

Maths >> Calculus >> Integrations IIT JEE

∫√tanx

Asked By: BONEY HAVELIWALA
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Joshi sir comment

let  √tanx = t

so sec2xdx/2√tanx = dt

so (1+t4)dx/2t = dt

so dx = 2tdt/(1+t4)

now solve

Maths >> Calculus >> Functions AIEEE

if ƒ:R−{0} -> R,  2ƒ(x) − 3ƒ(1⁄x) = x²  then ƒ(3)= ?

Asked By: BONEY HAVELIWALA
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Joshi sir comment

2ƒ(x) − 3ƒ(1⁄x) = x²   (1)

so 2ƒ(1/x) − 3ƒ(x) = 1/x²  (2)

multiply (1) to 2 and (2) to 3, then add the two equations, you will get f(x) then calculate f(3)  

Maths >> Calculus >> Functions Others

Sir/Madam,

                    Suddenly a question struck on my mind:   0×∞= 1 or 0?? as 1⁄0=∞.

     

Asked By: BONEY HAVELIWALA
is this question helpfull: 1 2 read solutions ( 2 ) | submit your answer
Joshi sir comment

it will be 0, assume it by considering that ∞ is a big number 

for ex.   0*(1111111111111111111111111) = 0

Maths >> Calculus >> Functions IIT JEE

FIND DOMAIN OF f(x)=log4log3 log2x WHERE 4,3,2 ARE BASES ?

Asked By: SIDDHANT
is this question helpfull: 4 0 submit your answer
Joshi sir comment

f(x)= log4log3log2

so 0 < log3log2x < 

so 1 < log2x < ∞ 

so 2 < x < 

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