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Find the value of x for which the function y = x\(^3\) - x has a minimum value.
Evaluate \(\int^{1}_{-2}(x-1)^{2}dx\)
Find the volume of solid generated when the area enclosed by y = 0, y = 2x, and x = 3 is rotated about the x-axis.
Evaluate: \(\int^{z}_{0}(sin x - cos x) dx \hspace{1mm}
Where\hspace{1mm}letter\hspace{1mm}z = \frac{\pi}{4}. (\pi = pi)\)
Find the area bounded by the curve y = x(2-x). The x-axis, x = 0 and x = 2.
From a point P, the bearings of two points Q and R are N67ºW and N23ºE, respectively. If the bearing of R from Q is N68ºE and PQ = 150m, calculate PR
Find the tangent to the acute angle between the lines 2x + y = 3 and 3x - 2y = 5.
In ∆MNO, MN = 6 units, MO = 4 units and NO = 12 units. If the bisector of angle M meets NO at P, calculate NP.
A man 1.7m tall observes a bird on top of a tree at an angle of 30°. if the distance between the man's head and the bird is 25m, what is the height of the tree?
Find a positive value of \(\alpha\) if the coordinate of the centre of a circle x\(^2\) + y\(^2\) - 2\(\alpha\)x + 4y - \(\alpha\) = 0 is (\(\alpha\), -2) and the radius is 4 units.
Divide 4x\(^3\) - 3x + 1 by 2x - 1
The first term of a geometric progression is twice its common ratio. Find the sum of the first two terms of the G.P if its sum to infinity is 8.
Express \(\frac{1}{x^{3}-1}\) in partial fractions
Three consecutive positive integers k, l and m are such that l\(^2\) = 3(k+m). Find the value of m.
Factorize completely \(x^{2} + 2xy + y^{2} + 3x + 3y - 18\).
A binary operation * is defined by a*b = ab+a+b for any real number a and b. if the identity element is zero, find the inverse of 2 under this operation.
If \(m*n = (\frac{m}{n} - \frac{n}{m}\)) for m, n belong to R, evaluate -3*4