What is the limit as t approaches 1 of 2ti-3j+e^tk ?

The limit as t approaches 1 of 2ti-3j+e^tk is (-3j+ek)+2i

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limit as t approaches 1 of 2ti-3j+e^tk

t \to 1 lim (2 t i - 3 j + e^{t} k)

(- 3 j + e k) + 2 i

Solution steps

t \to 1 lim (2 t i - 3 j + e^{t} k)

Plug in the value

t = 1

= 2 \cdot 1 i - 3 j + e^{1} k

Simplify

2 \cdot 1 i - 3 j + e^{1} k : (- 3 j + e k) + 2 i

= (- 3 j + e k) + 2 i

x \to 1 - lim (x^{2} + 3)

x \to 2 lim (3 x^{2} + 2)

x \to \frac{2}{3} lim (\frac{2 x ^{2} - 15 x + 18}{3 x ^{2} - 17 x - 6})

x \to 2 + lim (\frac{2 - 4 x}{x - 2})

x \to 1 + lim (\frac{∣ 1 - x ∣}{x - 1})

What is the limit as t approaches 1 of 2ti-3j+e^tk ?
The limit as t approaches 1 of 2ti-3j+e^tk is (-3j+ek)+2i