limit as t approaches 0 of e^{-7t}i+(t^2)/(sin^2(t))j+tan(3tk)

解

t \to 0 lim (e^{- 7 t} i + \frac{t ^{2}}{sin ^{2} ( t )} j + tan (3 t k))

j + i

解答ステップ

t \to 0 lim (e^{- 7 t} i + \frac{t ^{2}}{sin ^{2} ( t )} j + tan (3 t k))

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

不定形式の場合を除く

= t \to 0 lim (e^{- 7 t} i) + t \to 0 lim (\frac{t ^{2}}{sin ^{2} ( t )} j) + t \to 0 lim (tan (3 t k))

t \to 0 lim (e^{- 7 t} i) = i

t \to 0 lim (\frac{t ^{2}}{sin ^{2} ( t )} j) = j

t \to 0 lim (tan (3 t k)) = 0

= i + j + 0

簡素化

= j + i