Question 6 Evaluate the Given limit: lim(x--> 0) [(x+1)^5 - 1] / x
Class XI - Limits and Derivatives Page 301
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lim(x→0) [(x+1)⁵-1]/x
put x+1 = y
so
lim(y→1) = y⁵-1/y-1
we know lim(x→a) x^n - a/x-a = na^n-1
use it here
we get
lim(y→1) = y⁵-1/y-1
= 5.1^5-1
=> 5
so lim(x→0) [(x+1)⁵-1]/x = 5
put x+1 = y
so
lim(y→1) = y⁵-1/y-1
we know lim(x→a) x^n - a/x-a = na^n-1
use it here
we get
lim(y→1) = y⁵-1/y-1
= 5.1^5-1
=> 5
so lim(x→0) [(x+1)⁵-1]/x = 5
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