| utf19-006
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| utf19-008 For each of the following functions find an integer $n$ so that $ f( x) = 0$ for some $x$ between $n$ and $n+1.$ {(Recall the Intermediate Value Theorem)} \begin{alignat*}{2} a) f( x) &=x^3 -x + 3 & b) f( x) &=x^5+ x+1 \\ b) f( x) &=4x^2-4x+1 & d) f( x) &=x^5+5x^4+2x+1 \end{alignat*} |
| utf20-001 Fill in the derivatives. $$ a) \frac{d{\sin x}}{dx} b) \frac{d{\cos x}}{dx} c) \frac{d {\tan x}}{dx} d) \frac{d {\cot x}}{dx} e) \frac{d {\sec x}}{dx} f) \frac{d {\csc x}}{dx} $$ |
| utf20-002 Fill in the antiderivatives which you know up to now. $$ a) \int {\sin x dx} b) \int {\cos x} c) \int {\tan x} d) \int {\cot x} e) \int {\sec x} f) \int {\csc x} $$ |
| utf20-006 True or False. If False, make statement true (nontrivially).
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