Use continuity to evaluate the limit \lim_{x\to4}\frac{12+\sqrt{x}}{\sqrt

Finding original functions of second derivatives expressions
I have an antiderivative problem.
Given some function:
$f^{″}(t)=t+\sqrt{t}$
And the conditions when the $t=1$:
$f(1)=1;$
$f^{\prime }(1)=2$
How do I go about deriving the original function given that I must do this with antiderivatives? My logic has been to just take the antiderivative of the original f′′(t) and then take the antiderivative of f′(t) but I am wrong in this approach?

Differentiate ${\displaystyle y^2=4ax}$ w.r.t x(Where a is a constant)?

How do you find the instantaneous rate of change of the function $y=4x^3+2x-3$ when x=2?

${\displaystyle f\left(x\right)=4x^5-12x^4+5x^2+2x+2}$ concave or convex at ${\displaystyle x=-5}$?

trigonometry limits when x approaches zero
a) ${\displaystyle \underset{x\to 0}{lim}\frac{x}{\sin x}=1}$
b) ${\displaystyle \underset{x\to 0}{lim}\frac{\sin x}{x}=1}$
Is a) and b) true?
Because if I try to apply this to ${\displaystyle \underset{x\to 0}{lim}\sin 17\frac{x}{x}}$, my answer is 17, not 1

I'm having trouble solving this limit:
${\displaystyle \underset{x\to -2^{-}}{lim}\frac{1}{{(x+2)}^2}}$