Questions from General Calculus

Q: If the birth rate of a population is b (t)

If the birth rate of a population is b (t) = 2200e0.024t people per year and the death rate is d (t) = 1460e0.018t people per year, find the area between these curves for 0 < t < 10. What does this ar...

Q: A model rocket is fired vertically upward from rest. Its acceleration

A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a (t) = 60t, at which time the fuel is exhausted and it becomes a freely “falling” body. Fourteen s...

Q: Find the area of the shaded region. /

Find the area of the shaded region.

Q: Determine whether each integral is convergent or divergent. Evaluate those that

Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

Q: Graph f (x) = sin (ex) and use

Graph f (x) = sin (ex) and use the graph to estimate the value of t such that ft+1tf (x) dx is a maximum. Then find the exact value of t that maximizes this integral.

Q: Determine whether each integral is convergent or divergent. Evaluate those that

Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

Q: Determine whether each integral is convergent or divergent. Evaluate those that

Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

Q: Use the parametric equations of an ellipse, x = a cos

Use the parametric equations of an ellipse, x = a cos θ, y = b sin θ, 0 < θ < 2π, to find the area that it encloses.

Q: Find the area enclosed by the curve x = t2 – 2t

Find the area enclosed by the curve x = t2 – 2t, y = √t and the y-axis.

Q: Find the area enclosed by the x-axis and the curve

Find the area enclosed by the x-axis and the curve x = 1 + et, y = t – t2.