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find a cartesian equation for the curve. 𝜃 = 𝜋 6, find a linear function that models the data in the table. f(x) = x +, find an equation for the surface obtained by rotating the curve y = x about the x-axis., find dy dx and d2y dx2 . x = et, y = te−t, find dy dx by implicit differentiation. xey = x − y, find dy/dx and d2y/dx2. x = et, y = te−t, find equations of both lines through the point (2, −3) that are tangent to the parabola y = x2 + x., find f(–2) for the function f(x) = 3x2 – 2x + 7. −13 −1 1 23, find f(–2) for the function f(x) = 3x2 – 2x + 7., find f(g(−1)). f(g(−1)) =, find f(g(4)). f(g(4)) =, find f(x) such that h(x)= (fog)(x) and g(x) 7- x 7 x h(x)7-9 f(x) =, find the area enclosed by the curve x = t2 − 2t, y = t and the y-axis., find the area enclosed by the given parametric curve and the y-axis. x = t2 − 2t, y = t, find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(𝜃)., find the area of the largest rectangle that can be inscribed in the ellipse x2 a2 + y2 b2 = 1., find the area of the shaded region. r = 4 + 3 sin(𝜃), find the area of the shaded region. r = 𝜃, find the area of the shaded region. r2 = sin(2𝜃), find the area of the triangle def. area = square units, find the area of the triangle qrs. area = square units, find the derivative of the function using the definition of derivative. f(x) = mx + b, find the difference of functions s and r shown below. r(x) = –x² + 3x s(x) = 2x + 1 (s – r)(x) =, find the exact length of the curve. use a graph to determine the parameter interval. r = cos2 𝜃 2, find the exact length of the curve. use a graph to determine the parameter interval. r = cos2(𝜃/2), find the exact length of the curve. x = y4 8 + 1 4y2 , 1 ≤ y ≤ 2, find the exact length of the curve. x = y4 8 + 1 4y2 , 1 ≤ y ≤ 3, find the exact length of the curve. y = x − x2 + sin−1 x, find the exact length of the curve. y = x3 3 + 1 4x , 1 ≤ x ≤ 2, find the exact length of the curve. y = x3 3 + 1 4x , 1 ≤ x ≤ 3, find the exponential function f(x) = ax whose graph is given., find the exponential function f(x) = cbx whose graph is given., find the first partial derivatives of the function. f(x, y) = ax + by cx + dy, find the first partial derivatives of the function. z = x sin(xy), find the following angle measures. mangleead = ° manglecab = °, find the general solution of the given differential equation. 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