Solve this
Q. If $\underset{x\to 5}{\lim } f \left(x\right)=4 then \underset{y\to \frac{1}{3}}{\lim } f\left(15y\right)=$
(a) 1
(b) 1/3
(c) 5
(d) 4

Dear Student,

$$\begin{gathered} Given: \underset{x\to 5}{\lim } f\left(x\right) = 4 \\ Let x = 15y \\ \Rightarrow y = \frac{x}{15} \\ \therefore as x \to 5, \\ \frac{x}{15} \to \frac{5}{15}, or, y \to \frac{1}{3} \\ \therefore \underset{y\to \frac{1}{3}}{\lim } f\left(15y\right) \\ = \underset{x\to 5}{\lim } f\left(x\right) \\ = 4 \end{gathered}$$
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