How do you evaluate for x?

Question

lim_x->4
{x^2 - 8 x+16}/{x^4 -256}

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Answer 1 · 2018-03-17T02:22:29

#lim_(x->4)(x^2-8x+16)/(x^4-256) = 0#

Starting function:

#f(x) = (x^2-8x+16)/(x^4-256)#

Finding the limit:

#lim_(x->4) f(x) = lim_(x->4) (x^2-8x+16)/(x^4-256)#

Use L'Hospital's rule (take derivative of numerator and denominator and apply same limit):

#=lim_(x->4) (2x-8)/(4x^3)#

#= (2(4)-8)/(4(4)^3) = 0/256 = 0#