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1. Find dy dx if y =(5− 4x) 1 3 (2x + 7) 3 5 2. Find the equations of the tangent(s) to the curve y = x 2 that pass through (5,9). Provide a sketch in addition to your work. 3. Consider the trapezoid formed by the 4 lines x=0, y=0, y=12 and the tangent line to the curve y = 3x 2 − 36 at the point (4,12). Find the area of the trapezoid. 4. Find the equation of the normal line to y = 4 1− sin2 ( (3x)) 3 at x = 7π 6 . 5. Write the equation of the tangent to the curve defined by y = sin2 θ x = cosθ at the point where θ = π 3 6. Find the derivative of: f (x) = cos5x x 2 + 3 ⎛ ⎝ ⎜ ⎞ ⎠

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