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First seperate the function into the form A/(2+x) + B/(1-3x) + C/(1-3x) 2 . Find A B and C by equating the intergral to {A(1-3x) 2 +B(1-3x)(2+x) +C(2+x)}/(2+x)(1-3x) 2 . Cancelling the denominators gives an ...

The differential of tan(x) is sec 2 (x), however knowing how dy/dx tan(x)=sec 2 (x) is very useful in differentiating other trigonometric functions. So, if we first employ the rule that tan(x)=sin(x)/cos(x),...

Rearrange the first equation to get y on its own: y=-(1+4x) Substitute into the second equation: (1+4x)(1+4x)+5x^2+2x=0 21x^2+10x+1=0 Substite into the quadratic formula to solve (-b+/-(b^2-4ac)^0.5)/2a

a) To answer this question, one must be familiar with laws of logs, more sprecifically the rules when applied to the natural log of x, and exponentials (e). 2ln(2x+1) - 10 = 0 Step 1) 2ln(2x+1) = 10 Step 2) ...

To do this, first draw a sketch of both graphs to see roughly what kind of result we should expect to get. We know that at the intersection points, the values of x and y for both graphs must be equal. so set...