Question

Lim x tends to infinity (x+1/x)^x=y find the value of y .

Answer 1

Answer:

2

Step-by-step explanation:

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Answer 2

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y = x^x^x^x^-------infinite

we can write it-----

y = x^y

taking log both side

log y = log (x^y)

log y = y log x

taking differentiation both side with respect to x

d/dx (log y) = d/dx (y log x)

1/y*dy/dx = y* d/dx(logx)+logx*dy/dx

1/y*dy/dx = y / x+logx*dy/dx

dy/dx (1/y - logx) = y/x

dy/dx = y^2 / x(1 - y lox)