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Δ = b 2 - 4ac = q 2 - 4p (-4p) = q 2 + 16p 2 p different than 0 => 16p 2 greater than 0 only q 2 greater or equal to 0q 2 + 16p 2 > 0 => f has two ( 2 ) roots

We see a product of two things, so we should consider integration by parts (IBP). IBP is usually useful when either 1) you can differentiate or integrate one of the two things repeatedly to eventually get ze...

To differentiate we must use implicit differentiation. So: siny=x .Differentiating both sides we get (dy/dx)cosy=1 , so (dy/dx)=1/cosy . Using the common identity (sin 2 (y)+cos 2 (y)=1) we can rewrite the d...

First lets put all terms on the LHS;5 2x -5 x -5 = 0 (1);Now, to help us observe a pattern, put brackets on each term and separate power of x from its coefficients(5 x ) 2 - (5 x ) - 5 = 0 (2);Note that if w...

First, let's see how the plot of the functions looks like (draw on whiteboard). Next, let's calculate where the functions intersect by setting x 2 = sqrt(x) and solving for x (manipulate by squaring both sid...