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Let's remember what applying a modulus to any number actually does. Applying the modulus to a number just gives us back the positive version of that number- if it is positive, we get back itself, and if i...

(1) 4x² + y² - 25 = 0 (2) y - 2x - 1 = 0
Rearranging (2) into an equation of y in terms of x we have:y = 2x +1
now substituting into equation (1) 4x² + (2x +1)...

2y^1/2 -7y^1/4+ 3 = 0 We need to use a substitution to obtain a quadratic.Let y^1/4 = x (use the y with the smallest fractional power as your substitution)From this, we can s...

The product rule states that if y=uv, where u and v are both functions of x, then dy/dx = u(dv/dx) + v(du/dx)Therefore, the differential of 2xe^3...

Differentiating x² gives dx²/dx=2x. Differentiating a constant C gives 0. d( x² +C)/dx=dx²/dx+dC/dx=2x+0=2x. Since integration is the inverse function of differ...