Lim x—>16 x^¼-(16)^¼/(x-16) Answer the Value ?????

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Answer 1 · 2018-06-04T04:52:36

# 1/32#.

The easiest Solution is based upon the following

Standard Form of Limit : #lim_(x to a)(x^n-a^n)/(x-a)=na^(n-1)#.

With #a=16, n=1/4," the Limit"=1/4*(16)^(1/4-1)=1/4(2^4)^(-3/4)#,

#=1/4*2^-3=1/4*1/8=1/32#.

Otherwise, letting #x=y^4," as "x to 16, y to 2#.

#:."The Lim."=lim_(y to 2)(y-2)/(y^4-16)#,

#=lim(y-2)/{(y^2+4)(y^2-4)}#,

#=lim_(y to 2)cancel((y-2))/{(y^2+4)(y+2)cancel((y-2))}#,

#=1/{(2^2+4)(2+2)}#,

#=1/32," as before!"#