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A) Differentiate ln(x) b) integrate ln(x)

A) y=ln(x) E y = x E y (dy/dx ) = 1 E ln(x) (dy/dx) = 1 X(dy/dx) = 1 Dy/dx = 1/xb) y = 1 * ln(x) V = ln(x) U= x dv/dx =1/x Du/dx = 1xln(x) - (integral) x * (1/x)xln(x) - (integral) 1= xln(x) -x + C
SR
Answered by Stanley R. • Maths tutor
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a)Work out the total surface area of this cuboid (3cm x 4cm x 2cm). b) The cuboid has density 7g/cm^3, what is the mass of the cuboid?

a) The surface area of a 3 dimensional shape is the sum total of the area of each side of the shape. This cuboid is 3x4x2, and so it has 2 sides with area 3x4 = 12, 2 sides with area 4x2 = 8, and 2 sides wit...
LJ
Answered by Luke J. • Maths tutor
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Factorise fully the following expression: 2a^(2)b + 6ab^(2)

Factorise fully the following expression: 2a 2 b + 6ab 2 First, find the common terms by treating, 2a 2 b and 6ab 2 as separate objects. We see common terms of... 2, a, and b We notice that 2ab a = 2a 2 b an...
MW
Answered by Michael W. • Maths tutor
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(Follow on from previous question) A curve has equation y= x^2+3x+2. Use your previous results to i) find the vertex of the curve ii) find the equation of the line of symmetry of the curve

i) y = x 2 +3x+2 = (x+3/2) 2 -1/4Solution for (x+3/2) = 0 is x coordinate, which is x = -3/2Solution for y value is the additional constant, which is y = -1/4Therefore the vertex (minimum point) is (-3/2,-1/...
RI
Answered by Ross I. • Maths tutor
3701 Views

Express x^2+3x+2 in the form (x+p)^2+q, where p and q are rational numbers.

x 2 +3x+2 = (x+p) 2 +q (x+3/2) 2 = x 2 +3x+9/4 x 2 +3x+2 = (x+3/2) 2 -9/4+2 x 2 +3x+2 = (x+3/2) 2 -1/4
RI
Answered by Ross I. • Maths tutor
8488 Views