Find Limit of Function (2x - [[x]])?

Question

Find the limit of (2x - [[x]]) as x tends to 2 from the right side.

NOTE: [[x]] is the step function.

Answer 1

[[x]] is the greatest integer function

[[2.1]]=2

[[-3.4]]=-4



lim x-->2+ 2x-[[x]]



As x approaches 2 from the right, 2.01,2.001,2.00001, etc

2x approaches 4 and [[x]] approaches 2

The limit is 4-2 = 2



The limit approaches 2.

Answer 2

when 2 < x < 3 then [[x]] = 2, so the limit is lim/x->2+ (2x - 2) = 2

Answer 3

you should multiply via skill of (?(x²+x) + x) / (?(x²+x) + x) merely so the shrink will grow to be like this: lim (x??) (?(x²+x) - x)(?(x²+x) + x) / (?(x²+x) + x) lim (x??) (x² + x - x²) / (?(x²+x) + x) lim (x??) x / (?(x²+x) + x) you may now assemble x² in the sq. root and produce it out: lim (x??) x / (?[x²(a million+a million/x)] + x) lim (x??) x / (x*?(a million+a million/x)] + x) assemble x back: lim (x??) x / x*[?(a million+a million/x) + a million] = lim (x?+?) a million / [?(a million+a million/x) + a million] a million/x is going to 0 and also you've: lim (x??) a million / [?a million + a million] = a million/2