Questions from General Calculus

Q: (a). If we start from 00 latitude and proceed in

(a). If we start from 00 latitude and proceed in a westerly direction, we can let T (x) denote the temperature at the point at any given time. Assuming that T is a continuous function of x, show that...

Q: (a). The figure shows an isosceles triangle ABC with ∠

(a). The figure shows an isosceles triangle ABC with ∠B = ∠C. The bisector of angle B intersects the side AC at the point P. Suppose that the base BC remains fixed...

Q: Let T and N be the tangent and normal lines to the

Let T and N be the tangent and normal lines to the ellipse x2/9 + y2/4= 1 at any point P on the ellipse in the first quadrant. Let xT and yr be the x- and y-intercepts of T and xN and yN be the interc...

Q: Water is flowing at a constant rate into a spherical tank.

Water is flowing at a constant rate into a spherical tank. Let V (t) be the volume of water in the tank and H (t) be the height of the water in the tank at time t. (a). What are the meanings of V'(t)...

Q: Suppose f is a function that satisfies the equation f (x

Suppose f is a function that satisfies the equation f (x + y) = f (x) + f (y) + x2y + xy2 for all real numbers x and y. Suppose also that limx→0 f (x)/x = 1 (a). Find a (0). (b). Find f'(0). (c). Fi...

Q: For which positive numbers is it true that ax > 1 +

For which positive numbers is it true that ax > 1 + x for all x?

Q: The figure shows the graphs of f, f', and f''

The figure shows the graphs of f, f', and f''. Identify each curve, and explain your choices.

Q: Find points P and Q on the parabola y = 1 -

Find points P and Q on the parabola y = 1 -x2 so that the triangle ABC formed by the x-axis and the tangent lines at P and Q is an equilateral triangle. (See the figure.)

Q: Explain why the natural logarithmic function y = ln x is used

Explain why the natural logarithmic function y = ln x is used much more frequently in calculus than the other logarithmic functions y = logax.

Q: Atmospheric pressure P decreases as altitude h increases. At a temperature

Atmospheric pressure P decreases as altitude h increases. At a temperature of 150C, the pressure is 101.3 kilopascals (kPa) at sea level, 87.1 kPa at h = 1 km, and 74.9 kPa at h = 2 km. Use a linear a...