COMPUTING LIMITS WITH RATIONAL FUNCTION AND SQUARE ROOTS

Problem 1 :

x→3x-31x-13

Solution:

=x→3x-31x-13=x→3x-31x-13×3x3x=x→33x(x-3)3-x=x→3-(3x)=-3(3)=-9

Problem 2 :

x→01x+4-14x

Solution:

=x→01x+4-14x=x→01x+4-14x×4(x+4)4(x+4)=x→04-(x+4)x(4x+16)=x→0-xx(4x+16)=x→0-14x+16=-14(0)+16=-116

Problem 3 :

x→9x-3x-9

Solution:

=x→9x-3x-9=x→9x-3(x-9)×x+3x+3=x→9(x-9)(x-9)x+3=x→91x+3=19+3=13+3=16

Problem 4 :

x→0xx+4-2

Solution:

=x→0xx+4-2=x→0xx+4-2×x+4+2x+4+2=x→0xx+4+2x+4-2x+4+2=x→0xx+4+2x+4-4=x→0x+4+2=0+4+2=2+2=4

Problem 5 :

x→1x2-xx4-1

Solution:

=x→1x2-xx4-1=x→1(x2-x)x4-1×x2+xx2+x=x→1x4-xx4-1x2+x=x→1xx3-1x4-1x21+xx2=x→1x3-1xx4-1x2+xx2=x→1xx3-1x4-1x2+x=x→1x(x-1)x2+x+1x2+1x2-1x2+x=x→1x(x-1)x2+x+1x2+1(x+1)(x-1)x2+x=x→1xx2+x+1x2+1(x+1)x2+x=1(3)(2)(2)(2)=38

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