| utf28-008 Find all continuous functions $ f( x)$ which satisfy the equation $$( f( x))^2 = \int_{0}^{x}{{ f( t) \frac{t}{ 1+t^2}}} dt.$$ |
| utf29-009 Find the constant $k$ so that the graphs of $y=e^{4x}$ and $y=kx^2$ are tangent to one another at some point. |
| utf30-001 The density (weight per unit length) of a straight wire of length L varies along its length according to the formula $$ \delta( x) = kx +b \frac{\text{grams}}{ \text{cm}} (0 |
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| utf30-006 Show that $$\frac{1}{ 9} < \int_{{{-\sqrt 2}}}^{{{\sqrt 2}}}{e^{{-{x^2}}}} dx < 3.$$ What could you do to sharpen the upper and lower bounds of this integral? Sharpen them non-trivially. |