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Maths
A Level

What is the indefinite integral of xlog(x)?

The integral can be split into two different functions of x which is a hint that we must use the integration by parts method. The method is defined as

WH
Answered by William H. • Maths tutor
4439 Views

Using the binomial theorem, find the coefficient of x^4*y^5 in (x-2y)^9.

The term containing x4y5 will be C(9, 5)x4(-2y)5 = (9!/(5!4!))x4(-2)5y5The coefficient of which will be 1...

GH
Answered by George H. • Maths tutor
3624 Views

Using the trigonometric identity for tan(A + B), prove that tan(3x)=(3tan(x)-tan^3(x))/(1-3tan^2(x))

tan(3x)=tan(2x+x), by using the identity for tan(A+B)=(tan(A)+tan(B))/(1-tan(A)tan(B)),tan(3x)=tan(2x+x)=(tan(2x)+tan(x))/(1-tan(2x)tan(x)), using it again for tan(2x),tan(3x)=tan(2x+x)=([(tan(x)+tan(x))/...

IR
Answered by Ivan R. • Maths tutor
10374 Views

a curve is defined by y=2x^2 - 10x +7. point (3, -5) lies on this curve. find the equation of the normal to this curve

equation of tangent is y - y1 = m(x-x1). differentiating y gives us the value of m. so dy/dx = 4x-10. we know x is 3. therefore, dy/dx = m = 2 but we need equation of the normal, which is y-y1=(1/m)(x-x1)...

HH
Answered by Huy H. • Maths tutor
3597 Views

The curve C has an equation y = sin(2x)cos(x)^2. Find dy/dx. Find normal to curve at x = pi/3 rad, giving answer in exact form.

Student should use a combination of trigonometric identities, product rule and chain rule to find dy/dx.This can be done by applying product rule, obtainingdy/dx = sin(2x). d[cos(x)^2]/dx + cos(x)^2. d[si...

SC
Answered by Sunchi C. • Maths tutor
4114 Views

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