Questions from General Calculus

Q: Identify the curve by finding a Cartesian equation for the curve.

Identify the curve by finding a Cartesian equation for the curve.

Q: Determine whether the series is convergent or divergent by expressing sn as

Determine whether the series is convergent or divergent by expressing sn as a telescoping sum. If it is convergent, find its sum.

Q: Solve the initial-value problem y’ = 3x2 ey, y

Solve the initial-value problem y’ = 3x2 ey, y(0) = 1 and graph the solution.

Q: Find the orthogonal trajectories of the family of curves. /

Find the orthogonal trajectories of the family of curves.

Q: Find the orthogonal trajectories of the family of curves. /

Find the orthogonal trajectories of the family of curves.

Q: (a) Write the solution of the initial-value problem

(a) Write the solution of the initial-value problem and use it to find the population when t = 20. (b) When does the population reach 1200?

Q: Use series to evaluate the limit. /

Use series to evaluate the limit.

Q: (a) The population of the world was 6.1

(a) The population of the world was 6.1 billion in 2000 and 6.9 billion in 2010. Find an exponential model for these data and use the model to predict the world population in the year 2020. (b) Accord...

Q: Use Exercise 51 to find / Data from Exercise

Use Exercise 51 to find Data from Exercise 51: Use integration by parts to prove the reduction formula.

Q: One model for the spread of an epidemic is that the rate

One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of 5000 inhabitants...