I have exams coming up, and there are some problems from different homework assignments that I've had serious trouble understanding/figuring out how to do. I'd appreciate either a step-by-step, or just some help that will get me going. Thanks!
3. The equatorial radius of the earth is approximately 3960 miles. Suppose a wire is wrapped tightly around the earth at the equator. How much must this wire be lengthened if it is to be strung on poles 10 feet above the ground? (1 mile = 5290 feet).
4. Evaluate. You won't need the limit laws.
lim h-->0 (4root(3+h) - 2*(3+h) - 4root(3) + 6)/h
7. A particle starts moving along the x-axis from the point (100, 0 ), (distance in meters) and with an initial velocity of 25 m/min. If the acceleration is given by the equation a(t)=13*sqrt(t), what is the equation of motion of the particle?
8. A bocce ball is accidentally dropped from a building 98m high. How long does it take for the bocce ball to hit the ground, given that the acceleration due to gravity is 9.8 meters per second per second?
28. Evaluate the following indefinite integrals:
(c) integral 1/(sqrt(t)*(1-2*sqrt(t)))*dt
(d) integral 1/e^t *dt
32. Calculate the x-derivatives (derivatives w/ respect to x):
(d) d/dx * x/(x^2-2)
33. Find an anti-derivative of the function (t-1)^2/sqrt(t) that goes through the point (1,2)
42. Evaluate the indefinite integral ((1+x^2)/(1-x^2)^3)*x*dx.