MA212: Further Mathematical Methods (Calculus) 201314
Exercises 7: More improper integrals and the manipulation of proper integrals
For these and all other exercises on this course, you must show all your working.
1.
Determine whether each of the followin
MA212: Further Mathematical Methods (Calculus) 201314
Exercises 8: Leibnizs rule, the manipulation of improper integrals and LTs
For these and all other exercises on this course, you must show all your working.
1.
For x > 0, a function, f , is dened by
x2
MA212: Further Mathematical Methods (Calculus) 201314
Exercises 5: FTC (again), transformations and more double integrals
For these and all other exercises on this course, you must show all your working.
1.
The function, p(x, y ), of two variables is dene
MA212: Further Mathematical Methods (Calculus) 201314
Exercises 6: Improper integrals
For these and all other exercises on this course, you must show all your working.
1. Sketch a graph of f (x) = sin2 ( x) for x 0. (Or use Maple.)
From your picture, make
MA212: Further Mathematical Methods (Calculus) 201314
Exercises 3: Taylor series, more limits and the denition of the Riemann integral
For these and all other exercises on this course, you must show all your working.
1.
(a) Find the Taylor series expansio
MA212: Further Mathematical Methods (Calculus) 201314
Exercises 4: The fundamental theorem of calculus and double integrals
For these and all other exercises on this course, you must show all your working.
1.
Let f be a continuous function taking positive
MA212: Further Mathematical Methods (Calculus) 201314
Exercises 2: Approximate behaviour and convergence
For these and all other exercises on this course, you must show all your working.
1.
For x > 0, let f (x) = x ln 1 +
1
.
x
Evaluate f (x) for some lar
MA212: Further Mathematical Methods (Calculus) 201314
Exercises 1: Assumed background
The lectures do not cover practical techniques for integration of functions of a single variable as
students on this course are supposed to be skilled in this already. H