MATH137 Midterm: MATH137 Midterm 2 2014 Fall

• School: University of Waterloo
• Department: Mathematics
• Course: MATH137
• Professor: All

Document Summary

|x| tan 1 (cid:18) x2 x + 1 (cid:18) 1 (cid:19) x. X2 x 1 (cid:19: find the derivative of each function. (a) f (x) = (b) g(x) = x(ex + xe) x 1 x + 1 (cid:40) x2+2x 3. |x 1: find the equation of the tangent line to f (x) = x3 + 2x2 x at a = 1, let f (x) = Find all x where f (x) is continuous. 6. (a) state the domain and range of tanh x. (b) state the domain and range of tanh 1 x. (c) prove that tanh 1 x = (cid:18) 1 + x (cid:19) ln. 1 x: give an - proof that lim x 1 (1 3x) = 4, let f (x) = 2x2 + 3x. Show that there is a point on the graph of f that intersects the line y = x.