1. Let 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 can be determined from the weight using the formula . If there are 4 grams of solid at , estimate the amount of solid one second later.
2. Use Linear Approximation to approximate as follows: Let . The equation of the tangent line to at can be written in the form , where m=______ and b=______. Using this, the approximation of is _______.
3. The L.A. at x=0 of can be written as A+Bx where A=______ and B=______.
4. Use L.A. to approximate as follows: Let and find the equation of the tangent line to f(x) at a "nice" point near 1.003. Then use this to estimate .
5. The linearization at x=0 to is A+Bx . Compute A and B.
For number 4 I've gotten that it's approximately 0.997017919, but it keeps saying that it's wrong. I have no clue how to figure out any of the others.