## 1. Isolate GT1 in the equation . 2. True or False? ln (a + b) = ln a + ln b … prove your answer numerically. 3. What is the base-e logarithm of 250, ln 250? Prove that your result works numerically. 4. Solve for x in the following equation: e–ax = 1/T. 5. Simplify the right side of the function y = eAeC/eT and then use the ln to solve for T. 6. At what values of ϕ are the functions sin(ϕ) or cos(ϕ) equal to 0? At what values are they each equal to 1? 7. Linearize the following equation to find m and K from the slope and intercept: v = m[X]/(K + [X]). 8. Find the 1st and 2nd derivatives of y(x) = 3×4 – 2×2 + 15. 9. Identify the locations of minima and maxima for the function given in the problem above. 10. Find the derivative of the function y(x) = 3 ln (2×2). 11. Find the 1st and 2nd derivatives of Ψ(x) = (2/L)½ sin(nx/L). Then set all constants equal to 1.0 and plot Ψ(x), [Ψ(x)]2, Ψ’(x), and Ψ’’(x). 12. Integrate 3/x from to 1 to 3. 13. What is the integral of 3×2 – 2x + 4 between -1 and 1? 14. Integrate the following function from 2 to 4: y = 3 cos x + x/2. (Don’t forget to check your calculator settings! Is it set for degrees or radians?) 15. Isolate like terms and integrate both sides of your resulting differential equation: dy/dx = – 4 x-1 y-3.

No expert has answered this question yet. You can browse … Read More...