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Our example equation is, 5/[exp(x) + 6exp(-x)] - 1 = 0 ,and we wish to solve for x. Note that exp(x) is the same as writing ex I have chosen this one, because it helps illustrate some general g...
Label function: y=(cosx)/x2Recall quotient rule for functions of form h(x)=f(x)/g(x) given by,h'(x)=(f'(x)g(x)-f(x)g'(x))/(g(x))2Split original equation into f(x)=cosx and g(x)=xAnswered by Caelen D. • Maths tutor13711 Views
First differentiate the equation to find the equation of the tangents in terms of x. From this set dy/dx=0 because this is the stationary points, from this use the quadratic equation to find the value of ...
We use integration by parts. Set $u = x$ and $dv/dx = e^x$. This leads to $du/dx = 1$, and $v = e^x$. Then:\begin{align*}\int xe^x \mathop{\mathrm{d}x} &= xe^x - \int e^x \mathop{\mathrm{d}x}\&= x...
This is one of the most common a level math question. One which is essential to understand as it gives a firm understanding of core fundamental principles in math which are Completing the square and Algeb...
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