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Differentiate the following with respect to x.
b) f(x) = ln 2x . sin3 (x2 – 3)
A curve has an equation given by x2 – 2xy + y2 = 6.
a) Obtain an expression for dx dy in terms of x and y.
b) What is the gradient of the curve at (2, 3)?
Air is pumped into a spherical balloon such that the surface area of the balloon increases at a rate of 10 cm2 per second. Find the rate at which the radius is increasing when the radius is 4 cm. [ i.e. find when r = 4] [Note : surface area, A = 4πr2 ]
A body moves in a straight line and its displacement, s cm , from a fixed point P after a time , t, is given by the formula After t = 2 seconds, find its:
a) Displacement from P.
b) Velocity
c) Acceleration
Air is pumped into a spherical balloon such that the surface area of the balloon increases at a rate of 10 cm2 per second. Find the rate at which the radius is increasing when the radius is 4 cm. [ i.e. find when r = 4] [Note : surface area, A = 4πr2 ]
a. Find the orthogonal and normal canonical forms of 2y^2-2yz+2zx-2xy.
b. The operation,* defined by a*b= sin(ab), is a binary operation on N
True or false with full explanation
2 2 2 8 7 3 12 – 8 4 x y z xy yz zx
to the canonical form
through an orthogonal transformation and hence show that it
is positive Semi-definite.
Find the derivative of the function.
- Integrate[(Sqrt[t+Sin[t]]),{t,x,1}]
- Integrate[Sin[Power[t,4]],{t,2x,3x+4}]
Expand (2+x)^(-1/2) in ascending powers of x, up to the term x^3 . Hence approximate (2/3)^(1/2) correct to 3 significant figures
