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4-[(x+3)*((x-2)/(x^2 +5x +6))]

4-[(x+3)(x-2)/(x^2 +5x +6))]

factorise denominator 

4-[(x+3)(x-2)/(x+3)(x+2)]

cancel down (x+3)

4-[(x-2)/(x+2)]

expand 

4(x+...

dy/dx = 3x^2-2x+6

At (1,5), dy/dx = 7. 7 is the gradient of the tangent, therefore the gradient of the normal at (1,5) is -1/7.

An arithematic progression has terms in a sequence such that the difference between any two consecutive terms is a constant and is given by a common difference, say, d. If first term in the progression is...

The matrix is singular.

No inverse matrix.

Geometrically: No unique point of intersection of planes, Either no common point, a line of intersection or the three planes coincide.

Alege...

There are many methods to check it, but the the most useful is: By comparison: if we find a series whose terms are greater than the given ones which is known to be convergent (an armonic series for exampl...