Tutor profile: Alex K.

Why is it important to know your own learning style?

If you know your personal learning style, you will be able to best modify coursework to help yourself. For example, if you are a visual learner, redrawing figures from class will help solidify the material for yourself.

Find a linear approximation to f(x) = 3 x e^(2x−10) at x = 5.

First, find the derivative of the expression above. f′(x) = 3 e ^(2 x − 10) +6 x e^(2 x − 10) Then evaluate the function and the first derivative at 5. f(5) = 15 f′(5) = 33 The form for a linear approximation is: L(x) = f(x) + f'(x)(x - [value evaluated at]) Then, plug in the values: L(x) = 15 - 33(x - 5) L(x) = 33x - 150

Simplify the following expression: y(x + 3) - x(2y + 4) - 7x - 8y + 2

y(x + 3) - x(2y + 4) - 7x - 8y + 2 = yx + 3y - 2xy - 4x - 7x - 8y + 2 = -xy - 11x - 5y + 2