Unformatted text preview: Sample midterm I 1. Find the following indeﬁnite integrals (antiderivatives): √ a x − x2 dx 2 b x sin(x3 )dx √ c x+2 dx x 2. Find all the local minima and maxima (extrema) of the function f (x) = x2 ln(x) and indicate on which intervals f is increasing and on which intervals f is decreasing. √ 3. Let v (t) = t2 − t be the velocity of an object at time t. Compute the change of position in the object between times t = 1 and t = 2. 4. Find an equation of the line tangent to the curve y 2 + 4ey = 4x + ln(x2 ) at the point (1,0). 5. Let g (x) =
x a tan(x2 )dx. What is g (x)? 6. Let f (x) = 2x − 3sin(x) . Find f (x). 7. Where is the graph of f (x) = e−x concave down? 8. What is the area between the line y = 0 (the x-axis) and the parabola y = 1 − (x − 1)2 ? 9. Find the derivative of f (x) = xx .
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