a. In order to use differential equations, we must have equations with functions that not only are continuous, but also are differentiable. Name one natural process that is not differentiable everywhere. b. Consider the classic two-dimensional model for projectile motion in physics: X: = xo + vot cos 0 and y; = yo + vot sin 0 – gt². As you know, the ordered pairs (x¡, Y¡) (parametrized in time) trace a perfect parabola. No one questions whether this model is useful (even if we wish it included air resistance). However, this model is false. Why? Because it assumes that the earth is c. Sabine Hossenfelder said, "I find it hard to think of anything that's more relevant for understanding how the world works than " She goes on to say that these are fundamentally useful for understanding pandemics, the expansion of the universe, climate, financial markets, and quantum mechanics.

Are the functions †, g, and h given below linearly independent? g(x) = e 4x f(x) = e4 cos(5x), + cos(5x), h(x) = cos(5x). - they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial olution to the equation below. Be sure you can justify your answer. (et – cos(5æ)) + (et + cos(5x)) + - cos(5x)) = 0. help (numbers)

Let A be a positive constant. The equation of the line tangent to the curve sec(y) + x³ - 9 = Ay at the point (2, 0) is Oy=2 Y y = y = 12 A - 1 12 A (x - 2) y = 2x (x - 2) 12 31² - (22/2 + 2) X A A 9 A

Evaluate the following derivatives: a) d V1 + 4 + t° dt dx b) #CA 10 d dt dz 14 + 1 sin(z) c) d / V1 +P dt dx + Drag and drop an image or PDF file or click to browse...