Charles Darwin University
SMA 101 − Mathematics 1A
Tutorial 3
Q1 Find the following limit:
lim
x→0
sin x
1−cos x
Q2 (i) For the function f (x )=2 x
2
, find the average rate of change of f(x) with respect
to
x over the interval x0=0. 0 , x1=1 .0
(ii) Find the instantaneous rate of change of f(x) with respect to x at x0=0. 0
Q3 (i) For the function f (x )=1/ x
2
, find the average rate of change of f(x) with respect
to
x over the interval x0=1.0 , x1=2 .0
(ii) Find the instantaneous rate of change of f(x) with respect to x at x0=1. 0
Q4 (i) Write the formula for the slope of the tangent to the function f(x) at x = x0.
(ii) Using the formula in (i) find the slope of the tangent to the curve
f (x )=x2−5 at x = -1.
Q5 Using the definition of the derivative,
df
dx of a function f(x) with respect to x as:
df
dx
= lim
h→0
f ( x+h)−f ( x )
h
find
df
dx of f (x )=x
2−x
Q6 Find
dV
dr for
V (r )=4 π
3
r3

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