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Find the values of x for which f(x) is an increasing function given that f(x)=8x-2x^2

When a function is increasing, it’s derivative is positive. So first let us differentiate f(x). To differentiate x n we multiply by n and then reduce the power by 1. So f’(x)=8-2*2x=8-4x. We want to find the...
RL
Answered by Ruby L. • Maths tutor
12543 Views

Express 4sin(x)+6cos(x) in terms of Rsin(x+a) where R and a are constants to be determined (a should be given in rad).

R=sqrt(42)=6.48...a=arcos(4/sqrt(42))=0.905...Rsin(x+a)=6.48sin(x+0.905)
BU
Answered by Benjamin U. • Maths tutor
4610 Views

Integrate ln(x)

Take ln(x) = 1 * ln(x) and integrate by parts. Let u = ln(x) and dv/dx = 1 such that du/dx = 1/x and v = x. Using the integrating by parts formula, you get x ln(x) - integral(1) = x ln(x) - x + c.
JY
Answered by Jason Y. • Maths tutor
4311 Views

A ball of mass m moves towards a ball of mass km with speed u. The coefficient of restitution is 0. What is the final velocity if the first ball after the collision.

Coefficient of restitution is defined as the ratio of the relative speed of separation of the balls to the relative speed of approach. A ratio of 0 means that the speed of separation has a value of zero as t...
SE
Answered by Susannah E. • Maths tutor
3585 Views

Differentiate cos^2(x)

Using the chain rule, Let y=cos 2 (x)Let u=cos(x)y=u 2 dy/du=2udu/dx=-sin(x)dy/dx=dy/du*du/dx= -2sin(x)cos(x)
MB
Answered by Manish B. • Maths tutor
8003 Views