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First Step: I believe here it is important to firstly look at each equation on its own and just try to think how the examiner would want you to answer this type of question. Second Step: Recognise that both ...

4 cos 2 (x) + 7sin (x) – 7 = 0 (1) Using the identity sin 2 (x) + cos 2 (x) = 1, rearrange to give; cos 2 (x) = 1 - sin 2 (x) (2) Sub (2) into (1) ... Giving; 4 ( 1 - sin 2 (x) ) + 7sin (x) - 7 = 0 Expand br...

To find the factors of x 3 -7x-6, a method called equating coefficients can be used. Firstly, set the equation to zero and find a suitable number which satisfies the equation, in this case x=-1 satisfies the...

y=a^x take natural logs (also written as ln or log base e) of both sides lny=lna^x by logarithms rules lna^x=xlna lny=xlna Now differentiate implicitly 1/y = (dx/dy)lna Note here lna is just a constant, then...

There are a number of integrals that we can evaluate directly, called elementary functions:integral[ x dx ] = x 2 /2 + Cintegral[cos( x ) dx ] = sin( x ) + C However, most integrals cannot be solved so direc...