Search over 10,000 free study notes

This problem will be solved using the integration by parts method, taking the integrated function as udv which answer is uv-(integration of vdu) : u=x and dv=cos(x) so, du=dx and v=sin(x). We have, xsin(x...

the derivative of sinx is cosx, then we know that we can apply the product rule to find derivative of xsinx, such that if we let u=x and v=sinx and apply the formula d/dx(xsinx)=udv/dx+vdu/dx. to...

Firstly remember that each part of the equation can be differentiated separately. Let's label each part:

Part A: 2(x^2)y

Part B: 2x

Part C: 4y

Part D: -cos(piy)

Part E: ...

There will be intersection when x^2 + 4x + 3 = kx + 2. Our goal is to find the values of k which would only give one solution to this quadratic equation, which would make the lines 'tangent' to each other...

In plain english, we need to show that there is a value of x, which we call "a", in the interval 1 < a < 2 where f(a)=0. To prove this we start by letting x = 1: f(1) = 3 - 5(1) + 1^3<...