UFCalcSet15 - (a f x = x 2 sin x(b g x = e x x sin x 5...

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Exercises UF Calculus Set 15 1. Find the derivative of the given function. (a) f ( x ) = 2 sin( x ) + 3 cos( x ) (b) f ( θ ) = cos 2 ( θ ) (c) f ( x ) = x sin( x ) (d) f ( x ) = 3[ 2 - cot( x ) ] + 9 csc( x ) (e) f ( x ) = x 2 + x sin( x ) (f) f ( x ) = sin( x ) 1 + sin 2 ( x ) With the exception of part (e), determine all x in [ - π 2 , π 2 ] at which the graphs have horizontal tangents. 2. Find the derivative using the limit definition and the trigonometric sum identity formulas. (a) sin( αx ) , where α is a constant (b) tan( x ) 3. Find the equation of the tangent line to the curve at the given point: (a) y = x tan( x ) at the point with x -coordinate π 4 . (b) y = 2 e x cos( x ) at the point with x -coordinate 0 . (c) y = 2 sec 2 ( x ) at the point with x -coordinate π 4 . 4. Calculate the second derivative of the function.
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Unformatted text preview: (a) f ( x ) = x 2 sin( x ) (b) g ( x ) = e x ( x + sin( x )) 5. Evaluate the trigonometric limits: (a) lim x → sin 2 ( x ) 1-cos( x ) (d) lim x → sin 2 ( πx ) 3 x 2 (b) lim x → 1-sec( x ) 1-cos( x ) (e) lim x → π/ 2 cos( x ) 2 x-π (c) lim x → tan( x ) 2 x + sin( x ) 6. Write a formula for the derivative and sketch. Is the derivative function continuous? (a) f ( x ) = tan( x ) x < sin( x ) x ≥ (b) f ( x ) = cos( x ) x < 1-x x ≥ ——————————————————————-...
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This note was uploaded on 05/17/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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