Find the values of the constants A, B and C.
A hollow hemispherical bowl is shown in Figure 1. Water is flowing into the bowl. When the depth of the water is h m, the volume V m3 is given byV = 1/12 π h2(3 - 4h), 0 ≤ h ≤ 0.25
(a) Find, in terms of π, dV/dh when h = 0.1
Water flows into the bowl at a rate of π/800 m3s-1.
(b) Find the rate of change of h, in m s-1, when h = 0.1
The finite region R, shown shaded in Figure 2, is bounded by the curve, the x-axis and the line x = √2
The table below shows corresponding values of x and y for y = x3ln(x2 + 2)
(a) Complete the table above giving the missing values of y to 4 decimal places.
(b) Use the trapezium rule, with all the values of y in the completed table, to obtain an estimate for the area of R, giving your answer to 2 decimal places.
(c) Use the substitution u = x2 + 2 to show that the area of R is
(d) Hence, or otherwise, find the exact area of R.
5. Find the gradient of the curve with equation
ln y = 2x ln x, x > 0, y > 0
at the point on the curve where x = 2. Give your answer as an exact value.
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.