Practice Test 3b - function f x =(9 x 2 1 2 at the point(4...

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Prep Test IIIB for Calculus I, Math 1501C1, October 21, 2002 Name: This test is to be taken without calculators and notes of any sorts. The allowed time is 50 minutes. Write answers in boxes where provided. Provide exact answers; not decimal approximations! For example, if you mean 2 do not write 1 . 414 . . . .
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I: (20 points) Compute the derivatives of the functions a ) x tan( x ) b ) exp( x 3 ) c ) arccos(1 + x ) d) Let f ( x ) be a differentiable function. Calculate the derivative of f (1 - x ) f (1 + x ) at x = 0 . e) Let f ( x ) be a function with f (1) = 1 , f 0 (1) = - 2. Calculate the derivative of f ( x 2 f ( x 2 )) at x = 1 .
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II: (20 points) a) Find the equation of the tangent line to the graph of the
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Unformatted text preview: function f ( x ) = (9 + x 2 ) 1 / 2 at the point (4 , 5). b) Find the intersection of this tangent line with the x axis. III: (20 points) Water is dripping through the bottom of a conical cup 4 inches across and 6 inches deep. Given the cup loses half a cubic inch of water per minute, how fast is the water level dropping when the water is 3 inches deep? IV: (20 points) Find all the maxima and minima of the function cos( x )(cos( x ) + 1) in the interval [0 , 2 π ]. V: (20 points) How many roots has the equation 6 x 5 + 13 x + 1 = 0 ?...
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