How Does lim x--0(ex- 1 /x) =1Comes
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It can be proved using the expansion of e^x
e^x = 1 + (x/1!) +(x^2)/2! + (x^3)/3! +..... and so on
put this expansion of e^x in the above limit. 1 gets cancelled out by -1 and then x is taken as common from every term in the numerator and cancelled by the x in the denominator. Now the we can put the value of x=0 to get the limits as it is no longer an indeterminant form.
after putting x=0 we get the limit as 1
e^x = 1 + (x/1!) +(x^2)/2! + (x^3)/3! +..... and so on
put this expansion of e^x in the above limit. 1 gets cancelled out by -1 and then x is taken as common from every term in the numerator and cancelled by the x in the denominator. Now the we can put the value of x=0 to get the limits as it is no longer an indeterminant form.
after putting x=0 we get the limit as 1
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