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)limx→axn−anx−a=nan−1.
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)14−1=14(24)−34,
=1/4*2^-3=1/4*1/8=1/32=14⋅2−3=14⋅18=132.
Otherwise, letting x=y^4," as "x to 16, y to 2x=y4, as x→16,y→2.
:."The Lim."=lim_(y to 2)(y-2)/(y^4-16)∴The Lim.=limy→2y−2y4−16,
=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!"