Lim x ^ SiN x (x tends to 0 -)

Lim x ^ SiN x (x tends to 0 -)

limx∧sinx
＝lime∧(sinx＊lnx)
＝e∧（lim(sinx＊lnx)）
＝e∧（limx＊lnx）（x→0－,sinx～x）
＝e∧［limlnx/(1/x)］
= e Λ [LIM (1 / x) / (- 1 / X Λ 2)] (Law of lobita)
＝e∧limx(x→0-)
＝e°
＝1

Cos (70 + x) = 4 / 5, (180 < x < 270), sin (2x-40), urgent 5 questions
1. In this case, we can find out the following equation: 1
2. In triangle ABC, cosa * CoSb > Sina * SINB, judge the shape of triangle ABC
3、sin(x+π/3)+2sin(x-π/3)-√3cos(2/3π-x)
4. Tan α = log35 ^ 7, Tan β = log35 ^ 5, sin (α + β) - cos α cos β
5. Tan α and Tan β are the two roots of the equation 3x + 4x-2 = 0. Find sin (α + β) / [cos (α + β) - cos (α - β)]

1, cos (70 ° + x) = cos (- 70-x) = sin (90-70-x) = sin (20-x) = 4 / 5, thus cos (20-x) = 3 / 5, so sin (2x-40) = - 2Sin (20-x) cos (20-x) = - 24 / 252, cosa * CoSb > Sina * SINB, it is concluded that cosa * CoSb Sina * SINB = cos (a + b) > 0, thus 0 < A + B

(sin5π/12+cos5π/12)(sinπ/12-cosπ/12)

(sin5π/12+cos5π/12)(sinπ/12-cosπ/12)
=[sin(π/2-π/12)+cos(π/2-π/12)](sinπ/12-cosπ/12)
=(cosπ/12+sinπ/12)(sinπ/12-cosπ/12)
=sin²π/12-cos²π/12
=-(cos²π/12-sin²π/12)
=-cosπ/6
=-√3/2