If f(x) = cos x when x = npi (n = 0, 1, 2, 3, | vedclass

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(B) We need to find $\lim_{x 	o 0} f(\phi(x))$.First,let us evaluate $\lim_{x 	o 0} \phi(x)$.For $x 
eq 0$ and $x 
eq 3$,$\phi(x) = x^2 + 1$.As $x

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$3$

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(B) We need to find $\lim_{x 	o 0} f(\phi(x))$.First,let us evaluate $\lim_{x 	o 0} \phi(x)$.For $x 
eq 0$ and $x 
eq 3$,$\phi(x) = x^2 + 1$.As $x 	o 0$,$\phi(x) 	o 0^2 + 1 = 1$.Since $\phi(x)$ approaches $1$ as $x 	o 0$ (and $1 
eq 0, 1 
eq 3$),we look at the definition of $f(x)$ near $1$.Since $1$ is not of the form $n\pi$ for any integer $n \geq 0$,$f(x) = 3$ for values of $x$ near $1$.Therefore,$\lim_{x 	o 0} f(\phi(x)) = f(1) = 3$.

If $f(x) = \cos x$ when $x = n\pi$ $(n = 0, 1, 2, 3, \dots)$ and $f(x) = 3$ otherwise,and $\phi(x) = \begin{cases} x^2 + 1 & \text{when } x \neq 3, x \neq 0 \\ 3 & \text{when } x = 0 \\ 5 & \text{when } x = 3 \end{cases}$,then find $\lim_{x \to 0} f(\phi(x))$.

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