exam_180_1

# exam_180_1 - f of a function is given by r r r r r r r r r...

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MATH 180 Midterm exam September 23, 2005 Name: Section time: 1. Give the graph of f ( x ) = sin( x + π 2 ) - 1 over the interval [ - 2 π, 2 π ] as accurately as possible. (10pts) 1

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2. The half-life of a radioactive compound is 5.5 years. Find how many years it will take it to be reduced to 1% of its original quantity. (10pts) 2
3. Compute: (10pts ) lim x →-∞ 4 x 3 + 2 x 2 + x + 1 7 x 3 + x 2 - 1 4. Use the deﬁnition of the derivative to compute the derivative of f ( x ) = 1 x + 2 for x = 3. (10pts) Find the tangent to the graph of f at the same point. (10pts) 3

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5. The graph of the derivative
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Unformatted text preview: f of a function is given by: r r r r r r r r r r @ @ @ @ @ @ @ @± ± ± ± ± ± 2 6 9 10 4 8 i) Where is f increasing? ii) Where is f decreasing? iii) Where is f concave up? iv) Where is f concave down? v) Are there points in the interval (0 , 10) at which f is non-diﬀerentiable? Which? vi) Are there points in the interval (0 , 10) at which f is non-diﬀerentiable? Which? vii) Using the graph of f give an approximation for the graph of f (10pts each) 4...
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## This note was uploaded on 05/04/2008 for the course MATH 180 taught by Professor Tan during the Spring '08 term at Ill. Chicago.

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exam_180_1 - f of a function is given by r r r r r r r r r...

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