(a) Estimate the value of limx→0  ( (√(x2 + 9) ) – 3 )/ x2

(b) Evaluate:

(a)The area of the parabola y = x2 from (1,1) to (2,4) is rotated about the y-axis. Find the area of the resulitng surface.
(b) Find the solution of the equation y2dy = x2dx that satisfies the initial condition y(0) = 2.

As dry air moves upward, it expands and cools. If the ground temperature is 20°C and the temperature at a height of 1 km is 10C, express the temperature T(in °C) as a function of height h(in kilometers), assuming that the linear model is appropriate.

(a) What does the slope represent?

(b) Draw a graph of the function in part

(c) What is the temperature at a height of 2.5 km?

Integrate 

Find the Maclaurin series expansion of f(x) = e^x at x =0.

Find where the function f(x) = 3x⁴ – 4x³ – 12x² + 5 is increasing and where it is decreasing.

Find y’ if x³ + y³ = 6xy.

Show that y = x – 1/x is a solution of the differential equation xy’ + y = 2x.

Sketch the graph and find the domain and range of the function f(x) =2x-1.

Determine whether the series  converges or diverges.

If f(x,y) = x³ + x²y³ – 2y² , find f_x(2,1) and fy(2,1).

Show that the function f(x) = x² + √(7-x) is continuous at x = 4.