(Solved): Let \( y=5 x^{2}+2 x+4 \). If \( \Delta x=0.2 \) at \( x=3 \), use linear approximation to estimate ...

Let \( y=5 x^{2}+2 x+4 \). If \( \Delta x=0.2 \) at \( x=3 \), use linear approximation to estimate \( \Delta y \) \[ \Delta y \approx \] Let \( y=\tan (2 x+6) \). Find the differential \( d y \) when \( x=4 \) and \( d x=0.2 \) Find the differential \( d y \) when \( x=4 \) and \( d x=0.4 \) Let \( f(t) \) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid dissolves in such a way that the rate of change (in grams/minute) of the weight of the solid at any time \( t \) can be determined from the weight using the forumula: \( f^{\prime}(t)=-3 f(t)(4+f(t)) \) If there is 2 grams of solid at time \( t=2 \) estimate the amount of solid 1 second later. grams