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When a function is increasing, it’s derivative is positive. So first let us differentiate f(x). To differentiate xⁿ we multiply by n and then reduce the power by 1. So f’(x)=8-2*2x=8-4x. We wan...

R=sqrt(42)=6.48...a=arcos(4/sqrt(42))=0.905...Rsin(x+a)=6.48sin(x+0.905)

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.

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 a...

Using the chain rule, Let y=cos²(x)Let u=cos(x)y=u²dy/du=2udu/dx=-sin(x)dy/dx=dy/du*du/dx=-2sin(x)cos(x)