1. Let $\displaystyle f(t)$ 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 can be determined from the weight using the formula $\displaystyle f'(t)=-3f(t)(5+(f(t))$. If there are 4 grams of solid at $\displaystyle t=2$, estimate the amount of solid one second later.

2. Use Linear Approximation to approximate $\displaystyle 1.6^4$ as follows: Let $\displaystyle f(x)=x^4$. The equation of the tangent line to $\displaystyle f(x)$ at $\displaystyle x=2$ can be written in the form $\displaystyle y=mx+b$, where m=______ and b=______. Using this, the approximation of $\displaystyle 1.6^4$ is _______.

3. The L.A. at x=0 of $\displaystyle Sqrt(3+5x)$ can be written as A+Bx where A=______ and B=______.

4. Use L.A. to approximate $\displaystyle 1/1.003$ as follows: Let $\displaystyle f(x) = 1/x$ and find the equation of the tangent line to f(x) at a "nice" point near 1.003. Then use this to estimate $\displaystyle 1/1.003$.

5. The linearization at x=0 to $\displaystyle sin(6x)$ 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.