(a) Find the gradient of the curve at P.
(b) Hence find the equation of the normal to C at P, giving your answer in the form ax + by + c = 0, where a, b and c are integers.
(b) Using your answer to part (a), find ∫x2 cos 3x dx
1/(2 - 5x)2, |x| < 2/5
in ascending powers of x, up to and including the term in x2, giving each term as a simplified fraction.
Given that the binomial expansion of (2 + kx)/(2 - 5x)2, |x| < 2/5 is
1/2 + 7/4x + Ax2 + ...
(b) find the value of the constant k,
(c) find the value of the constant A.3 (a) Binomial Expansion
Figure 1 shows the curve with equation
y = [2x/(3x2 + 4)], x ≥ 0
The finite region S, shown shaded in Figure 1, is bounded by the curve, the x-axis and the line x = 2
The region S is rotated 360° about the x-axis.
Use integration to find the exact value of the volume of the solid generated, giving your answer in the form k ln a, where k and a are constants.Volume of Revolution
Figure 2 shows a sketch of the curve C with parametric equations
x = 4 sin (t + π/6), y = cos 2t, 0 ≤ t < 2π
(a) Find an expression for dy/dx in terms of t.
(b) Find the coordinates of all the points on C where dy/dx = 05 (a) Parametric Curves More Questions
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.