Determine the limit of each function analytically. Show neat and complete solution. (hint: some of the items need to be factored or rationalized for the limits to exist) limx→−4(x+4)2x2−16

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Determine the limit of each function analytically. Show neat and complete solution. (hint: some of the items need to be factored or rationalized for the limits to exist)  limx→−4(x+4)2x2−16

ensojadasH · Accepted Answer

Limit: If the value of a function f(x) approaches to L as the input approaches to c from both directions, then the limit of the function f(x) at x=c is L.  The difference of the squares of two varibles is defined as:  a2−b2=(a−b)(a+b)  The square of any variable is the product of the variable with itself.  x2=x⋅x  The given limit problem is:  limx→−4(x+4)2x2−16  We need to find the limit of the function analytically.  The given limit problem can be written as:  limx→−4(x+4)2x2−16=limx→−4(x+4)2x2−42  =limx→−4(x+4)(x+4)(x−4)(x+4)  =limx→−4x+4x−4  Applying the limit, we get  limx→−4(x+4)2x2−16=(−4+4)(−4−4)  =0−8  =0  Answer: The limit of the given function is limx→−4(x+4)2x2−16=0

Jeffrey Jordon · Accepted Answer

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Determine the limit of each function analytically. Show neat and complete soluti

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