MAS120 - Applied Mathematics - Science and Math's Assignment Help

Assignment Task

1.(a) Graph the function f(x) = 1/x

(b) Hence, using translations, reflections etc., graph f(x) = 1 + 1 2 − x Make sure that you show and label the intermediate graphs.

2. For each of the following functions, give the domain and range using interval notation, showing your reasoning. (When the domain is not specified, we adopt the convention that the domain consists of all numbers for which the function is defined.) (a) f(x) = √ x−2 9−x2 (b) f(x) = √ x 2 + x − 2

3. Find the following limits, if they exist, showing all the working. (a) limx→1 3x 2 − 2x − 1 x − 1 (b) limx→∞ 5x 3 + 2x − 4 1, 500 − 2x 3

5.  Find the derivatives of the following functions, simplifying your answers. (a) f(x) = (3 − 2x 2 ) √ x + x 1/3 (b) y(x) = x 2−2 x2+4 (c) g(t) = (t 4 + 1)(t 3 − 2)4/3

6.  Find (and simplify) the equation of the tangent line to the graph of y = 5x x−3 at x = 2.

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