Given problem lim θ → 0 sin ⁡ θ 3 θ + tan ⁡ θ I got to lim θ → 0 sin ⁡ θ cos ⁡ θ 3 θ cos ⁡ θ + sin ⁡ θ Now I'm lost. Any advice on how to be more efficient?

Question

Given problem      lim          θ      →      0                  sin      ⁡      θ              3      θ      +      tan      ⁡      θ      I got to      lim          θ      →      0                  sin      ⁡      θ      cos      ⁡      θ              3      θ      cos      ⁡      θ      +      sin      ⁡      θ      Now I&#039;m lost. Any advice on how to be more efficient?

boomzwamhc · Accepted Answer

Hint : divide both side to   θ and note that      lim          θ      →      0                          sin        ⁡                  θ                    θ        =  1        lim          θ      →      0                          tan        ⁡                  θ                    θ        =  1

aligass2004yi · Accepted Answer

Hint:You can write it as:      lim          θ      →      0                  sin      ⁡      θ              sin      ⁡      θ              (                              3            θ                                sin            ⁡            θ                          +                  1                      cos            ⁡            θ                          )              =      lim          θ      →      0            1                            3          θ                          sin          ⁡          θ                    +              1                  cos          ⁡          θ

Given problem <munder> <mo movablelimits="true" form="prefix">lim <mrow class="MJX-T

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