Rewriting this limit into a derivative:
$$\lim_{h\rightarrow 0} \dfrac{sec(\pi + h) + 1}{h}$$
Looks like it came from:
$$\lim_{h\rightarrow 0} \dfrac{f(a + h) - f(a)}{h}$$
I have to ask:
a=?
f(a+h)=?
So,
a = $\pi$
f(a + h) = sec($\pi$ + h)
therefore,
f(a) = Sec($\pi$) = -1
Plugging it...
I factored the largest factor of x from the polynomial and got:
lim $x^3$=∞
x->∞
and
lim $(-2+\dfrac{3}{x^2}-\dfrac{4}{x^2})$=-2
x->∞
Would that make the:
lim arctan (-2) =lim arctan($-2x^3+3x-4$)
x->∞...x->∞Edit: I just realized that:
lim $-2x^3+3x-4$ = -∞
x->∞
Therefore,
lim...