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Multiply equation 1) by 2 : 12a+2b=32. There are alternate signs of b and so therefore add the equations together: 17a=51. Solve for a: a=3. Sub a into one of the equations to find b: 5*3-2b=19b=-2. The fina...

First, we need to find the derivative f'(x) for all x, and then we will substitute x=2π into the function we find. To do this, we need to set up our limit: f'(x) = lim [sin(3(x+h))-sin(3x)]/h as h-> 0 We ...

Expand by multiplying out the brackets (using crab claws or similar method): 18x^2 + 30x - 12x -20Simplify by combining like terms: 18x^2 + 18x -20

Base Case n=1sum_1(r 3^(r-1))=1 3^0=1=1/4+(3^1/4) (2-1)=1/4+3/4=1 Assume true for n=ki.e. sum_k(r 3^(r-1))=(3^k/4) (2k-1) then for n=k+1sum_(k+1)(r 3^(r-1))= sum_k(r 3^(r-1))+(k+1) 3^k =(3^k/4) (2k-1)+(k+1) ...

This question challenges the student's ability to use the chain rule and to understand what a stationary point is. Having recognised that the chain rule is required, the first step is to use the substitution...