Jawaban:

limit

..

1).

lim x → 0

= (1 – √1 + x)/(x² – x)

lim x → 0

= (1 – √1 + x)/(x² – x) . (1 + √1 + x)/(1 + √1 + x)

lim x → 0

= (1 – √1 + x)(1 + √1 + x)/(x² – x)(1 + √1 + x)

lim x → 0

= (1 – (1 + x))/ (x² – x)(1 + √1 + x)

lim x → 0

= (1 – 1 – x)/(x² – x)(1 + √1 + x)

lim x → 0

= (-x)/ x(x – 1) (1 + √1 + x)

lim x → 0

= -1/(x – 1)(1 + √1 + x)

= -1/(0 – 1)(1 + √1 + 0)

= -1/(-1)(1 + √1)

= -1/(-1)(1 + 1)

= -1/(-1)(2)

= -1/(-2)

= 1/2

……..

2).

lim x → 0

= x/(√1 + x) – (√1 – x)

lim x → 0

= x/(√1 + x) – (√1 – x) . (√1 + x) + (√1 – x) /(√1 + x) + (√1 – x)

lim x → 0

= x(√1 + x) + (√1 – x)/(√1 + x) – (√1 – x)(√1 + x) + (√1 – x)

lim x → 0

= x(√1 + x) + (√1 – x) / (1 + x) – (1 – x)

lim x → 0

= x(√1 + x) + (√1 – x) / (1 – 1 + x + x)

lim x → 0

= x(√1 + x) + (√1 – x)/(2x)

= x(√1 + x) + (√1 – x) / x(2)

= (√1 + x) + (√1 – x)/2

= (√1 + 0) + (√1 – 0)/2

= (√1 + √1)/2

= (1 + 1)/2

= 2/2

= 1