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# 2 10 pts a using complete sentences and appropriate

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2. (10 pts.) (a) Using complete sentences and appropriate notation, state the Intermediate Value Theorem. (b) Show that the equation has at least one solution in x 3 x 2 2 x 1 the interval [-1,1]. ______________________________________________________________________ 3. (5 pts.) Pretend f is a magical function that has the property that at x = 3 the tangent line f is actually defined by the equation y = -2(x - 1) + 5. Obtain (a) f (3) = (b) f (3) =

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TEST2/MAC2311 Page 2 of 4 ______________________________________________________________________ 4. (25 pts.) Compute the first derivatives of the following functions. You may use any of the rules of differentiation that are at your disposal. Do not attempt to simplify the algebra in your answers. (a) f ( x ) 4 x 6 7 x 12 8tan( x ) f ( x ) (b) g ( x ) (4 x 2 2 x 1 )sec( x ) g ( x ) (c) h ( t ) 5 t 10 1 sin( t ) 2 h ( t ) (d) y cot 5 (2 θ 1) dy d θ (e) L ( z ) sin(4 z 8 ) 4 csc ( π 6 ) 4cos( z 2 ) dL dz ( z )
TEST2/MAC2311 Page 3 of 4 ______________________________________________________________________ 5. (10 pts.) What are the x- and y - intercepts of the tangent line to the graph of y = 1/x 2 at the point (2,1/4)? ______________________________________________________________________ 6. (10 pts.) (a) Find all values in the interval [0,2 π ] at which the

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2 10 pts a Using complete sentences and appropriate...

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