Test 3 sols - TEST 3 SOLUTIONS 1[6 pts Use the QUOTIENT...

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1 TEST 3 SOLUTIONS 1[6 pts] Use the QUOTIENT RULE to find ( f x : ( 29 cot 1 csc x f x x = ( 29 ( ( ( ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 3 2 2 2 2 3 2 2 2 2 2 1 csc csc cot csc cot csc csc csc cot 1 csc 1 csc csc csc csc csc 1 csc 1 csc csc csc csc 1 csc 1 csc 1 csc 1 csc x x x x x x x x x f x x x x x x x x x x x x x x x x + - - - - - + = = + + - - + - - + - - - = = = = + + + + 2[6 pts] Find dy/dx: sin cos ; cos sin sin cos 2sin dy y x x x x x x x x x x dx = - = + + = + 3[6 pts] Find the equation of the line tangent to ( cos 3 at y x x x π = = Recall that the slope is dy dx : ( 29 tan 3 sin 3 cos3 ; 1 x dy dy x x x m dx dx π = = - + = - = and at , x y π π = = - so the equation of the tangent is ( ; y x y x π π = - - = - 4[6 pts] Find ( f x : ( 29 ( 29 ( 29 ( 29 ( 29 2 2 3 2 2 3 2 7 7 ; 2 7 1 14 f x x x x f x x x x x - - - - - - = - = - = - - + 5[6 pts] Find dy/dx by implicit differentiation: 2 3 3 3 x y xy x - = ( 29 3 2 2 3 2 2 3 2 2 1 2 3 2 9 3 1 0 ; 9 1 2 3 ; 9 dy dy dy dy xy y x xy xy y x xy xy y dx dx dx dx x xy - - + + + - = + = - - = + 6[8 pts] Find BY IMPLICIT DIFFERENTIATION 2 2 d y dx : 3 3 4 0 x y - = You may leave the answer with y but not dy/dx in it.
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