Answer to Question #189369 in Calculus for clarisse

Question

Your classmate requests you to help him/her in understanding the solutions of the

lim

t→0

(1−cos3t)/

(3t)

= 0, via writing. How do you apply your knowledge based on what you have

learned from this module in doing the task?

Answer 1

Ans:-

$\lim_{t \to 0} \dfrac{1-Cos3t}{3t}\\ \Rightarrow \lim_{t \to 0} \dfrac{1-(1-2Sin^23t)}{3t}\\ \Rightarrow\lim_{t \to 0} \dfrac{2Sin^23t}{3t}\\ \\$

$\Rightarrow \lim_{x \to 0} 2\times\dfrac{Sin^23t\times3t}{(3t)^2}\\ \Rightarrow\lim_{t \to 0}6t\lim_{t \to 0} \dfrac{Sin^23t}{(3t)^2}$ $\because \lim_{t \to 0} \dfrac{Sint}{t}=1$

$\Rightarrow \lim_{t \to 0}6t \times1$ $\because \lim_{t \to 0} \dfrac{Sin^23t}{(3t)^2}=1$

$\Rightarrow 0$ .....Ans