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

1 Answer
Jun 4, 2018

1/32132.

Explanation:

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)limxaxnanxa=nan1.

With a=16, n=1/4," the Limit"=1/4*(16)^(1/4-1)=1/4(2^4)^(-3/4)a=16,n=14, the Limit=14(16)141=14(24)34,

=1/4*2^-3=1/4*1/8=1/32=1423=1418=132.

Otherwise, letting x=y^4," as "x to 16, y to 2x=y4, as x16,y2.

:."The Lim."=lim_(y to 2)(y-2)/(y^4-16)The Lim.=limy2y2y416,

=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!"