- Find the area bounded between the following curves.
- \(x = -2\), \(x = 1\), \(y = 2x^2 + 5\), \(y = 0\).
- \(x = 2\), \(x = 4\), \(y = \frac{x-1}{4}\), \(y = \frac{1}{x-1}\).
- \(y = x^5 - 2\ln(x+5)\), \(y = - 2\ln (x + 5)\).
- \(x = 0\), \(x = 3\), \(y = e^x\), \(y = e^{4-x}\).
- Use implicit differentiation to find a formula for \(dy/dx\) in each
of the following. (Your answer may include both \(x\) and \(y\).)
- \(6x^2 + 5y^2 = 36\).
- \(3x^2 = \frac{2-y}{2+y}\)
- \(10\sqrt{x}+6\sqrt{y} = 8y\).
- Find the equation of the tangent line at the given point on each curve.
- \(x^2+y^2=25\) at \((-3,4)\).
- \(x^2y^2 = 81\) at \((-1,9)\).