calculus

MAT1236D Calculus I
Trimester 2, 2014 Assignment 1: functions and di?erentiation Due: Wednesday 2 July at 2pm This assignment is worth 30 marks and will comprise 10% of your ?nal grade. The number of marks assigned to each question is listed in the right margin. Please write your answers in pen, show full working, and staple your papers together before submitting your assignment in class next Wednesday.
1. Find the derivative dy of the following functions. dx (2) (2) (2) (3) 1 2 ln x (3) (3) v x2 1 ln . 2 x+1

(a) y = [(x – 1)(x + 1)]8 (b) y = 1 + tan x sin x 1 + x2 x2
5x

(c) y = ln
v

(d) y = e

(e) y = x cosh x + v (f) y = sin-1 x

2. Consider the function f (x) =

sin x +

(In this course, the value of x in a trigonometric function such as sin x should always be treated as a value in radians.) (a) What is the value of the function at x = (b) For what values of x is sin x positive? (c) What is the domain of f ? (Hint: Try plotting the function using a computer or graphics calculator.) (d) Find the derivative f (x) of f . (Hint: Use logarithm laws to simplify f (x) before di?erentiating it.) (e) What is the domain of f ? (f) Find the equation for the tangent and normal line to the curve at x = p . 2 p ? 2 (1) (2) (3)

(3)

(3) (3)

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