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Integrate xcos(x)

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)-i...
LA
Answered by Lucia A. • Maths tutor
4156 Views

Find the derivative of sinx, use that to find the derivative of xsinx

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)=u dv/dx+v du/dx. to obtain xc...
NB
Answered by Niren B. • Maths tutor
5165 Views

Implicitly differentiate the following equation to find dy/dx in terms of x and y: 2x^2y + 2x + 4y – cos (piy) = 17

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: 17 Parts B and E are easy to different...
NK
Answered by Nikhil K. • Maths tutor
7415 Views

Find two values of k, such that the line y = kx + 2 is tangent to the curve y = x^2 + 4x + 3

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. F...
AN
Answered by Andrew N. • Maths tutor
35969 Views

Given f(x) = 3 - 5x + x^3, how can I show that f(x) = 0 has a root (x=a) in the interval 1<a<2?

In plain english, we need to show that there is a value of x, which we call &quot;a&quot;, in the interval 1 &lt; a &lt; 2 where f(a)=0. To prove this we start by letting x = 1: f(1) = 3 - 5(1) + 1 3 = -1. W...
GP
Answered by Giorgos P. • Maths tutor
8200 Views