Calculus 1000A/B Lecture Notes - Lecture 11: Differentiable Function, University Of Manchester, 32X

• School: Western University
• Department: Calculus
• Course: Calculus 1000A/B
• Professor: Pei Yu

Document Summary

Example. (x3 + x) = 3x2 + 1 (x3+x) = ((x3+x) ) = (3x2+1) = (3x2) +1 = 3(x2) +0 = 3 2x = 6x (x3+x) = (x3+x)(3) = (((x3+x) ) ) = ((x3+x) ) = (6x) = 6x = 6 1 = 6. For f (x) = xex nd f (x) and f (x). f (x) = (x. The equation of motion is s = f (t) = t 1 t, where s is position (in meters), t is time (in seconds). Find the velocity and speed when t = 5. We know: velocity is f (t), speed is |f (t)| (in m/sec). f (t) = (t 1 t) = (t 1) t = ( 1)t 1 1 1 = t 2 1 = . 1 t2 1(cid:12)(cid:12)(cid:12) f (5) = . If h(x) = f (x) g(x) , f (4) = 2, g(4) = 5, f (4) = 6, g (4) = 3, nd h (4).