| ucf09-005 This problem is from Professor Addison's Fall 1974 Math 1A midterm: A giddily gleeful witch, elated over passing her Mathematics 1A midterm examination, hurls a somewhat overripe pumpkin directly upward from the ground. It moves according to the law \( s(t) = 96t - 16t^{2} \), where \( t \) is the time in seconds after it is thrown and \( s(t) \) is its height in feet above the ground at time \( t \). Find:
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| utf04-007 Compute the following limits (think about the {theorems} you use). \begin{alignat*}{3} &a) \lim_{x\to 1} \frac{x^3-1 }{ (x-1)^2} & &b) \lim_{x\to{-2}} \frac{x^3 + 8 }{ x+2} & &c) \lim_{x \to 1} \frac{x^3-2x^2 + 2x -1 }{ x^3 -1} \\ &d) \lim_{x\to 8} \frac{\root 3 \of x - 2 }{ x-8} & &e) \lim_{x\to{-1}} \frac{\frac{1}{ x}+ 1}{x+1} & &f) \lim_{x \to a} \frac{x^n - a^n }{ x-a} \\ &g) \lim_{x\to 2} \frac{\sqrt 2 - \sqrt x }{ 2-x} & &h) \lim_{x \to 0}\frac{1- \sqrt{1-x^2} }{ x^2} & &i) \lim_{x \to 4} \frac{\root 3 \of x - \root 3 \of 4 }{ x-4} \end{alignat*} |
| utf06-001 Recall that $\sin^2 x = 1- \cos^2 x$. Write an expression for each trig function squared in terms of one of the other trig functions. $$a) \cos^2 x b) \tan^2 x c) \cot^2 x d) \sec^2 x e) \csc^2 x$$ |