Evaluate the limit, if it exists. showing clearly the steps lim h→0 (4 + h)3 − 64 h?

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Answer 1 · 2018-04-24T18:10:55

# 48#.

I presume the Question is to find #lim_(h to 0){(4+h)^3-64}/h#.

Knowing that, #(a+b)^3=a^3+b^3+3ab(a+b)#, we have,

#(4+h)^3=4^3+h^3+3*4*h(4+h)#,

#=64+h^3+48h+12h^2#.

#:. (4+h)^3-64=h^3+12h^2+48h=h(h^2+12h+48)#.

#:. {(4+h)^3-64}/h=h^2+12h+48, h!=0#.

#:."The Reqd. Lim."=lim_(h to 0){(4+h)^3-64}/h#,

#=lim_(h to 0)h^2+12h+48#,

#=0^2+12xx0+48#,

#=48#.