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

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

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

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

j + i

Solution steps

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)

With the exception of indeterminate form

= 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

Simplify

= j + i

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\int 2 x^{3} \cdot e^{- x^{2}} d x

y^{^{''}} + 4 y = 8 cos (2 x)

\frac{d y}{d t} = k y (1 - y)

\int x x^{2} + 5 d x

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