\%VY \( \left\|_{11_{0}}{ }_{+\uparrow}^{++}\right\|_{1,}+ \) - ?) \( \sim 1 \cdot: \varepsilon \) Please show all your work Q1) The inequality \( -4 \leq x \leq 10 \) can be expressed in the form \( |x-a| \leq b \) Find \( a \) and \( b \) Q2) Let \( f(x)=\frac{1}{1+\frac{1}{1+\frac{1}{x}}} \). Then: Find the domain of \( f \) Q3) Let \( g(x)=3 x-2 \). Find a function \( f \) such that \( (f \circ g)(x)=18 x^{2}-36 x+19 \). Q4) Evaluate \( \lim _{x \rightarrow 0} \frac{\sqrt{|x|} \cos \left(\pi^{1 / x^{2}}\right)}{2+\sqrt{x^{2}+3}} \) (if it exists). Give a careful proof that your conclusion is correct. Q5) [6pts] Find a point a such that the tangent line to the graph \( y=\sqrt{x} \) at a has \( y \)-intercept 3
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The midpoint is \( a = \frac{-4 + 10}{2} = 3 \), and the distance to the endpoints is \( b = \frac{10 - (-4)}{2} = 7 \). So the inequality can be expressed as \( |x-3| \leq 7 \). Answer: \( \boxed{a=3, b=7} \) Q2) Show more…
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