Transcribed Text
1.
b
Evaluate the following limits:
I2 2
x²2
i)
lim
ii)
lim
iii

z+1* x 1
x
z++00
I' 2
I2
iv
lim
v
lim
vi
lim 
z++00 3x³ 1
1>00 3x³ 1
r>00
I' 2
I 2
x²3x4
vii
lim
vil
lim
ix
z++00 3.5 1
z>00 3r¹ 1
z+4 x4
lim
2.
(c)
Find a value of K so that the function f(x) is continuous at x = 0 where
sinz
+ K(x3)²,
<0,
f(x)
x


3.
@  =  Calculate lim
Af
A+0 h
by
Evaluate lim tan(2x)
r+0 sin(4x)
C
Evaluate lim
z++00
b Use the definition of derivative to find j'(2) for f(x) = I2  3x.
c
Find the equation of the tangent line of the graph of the function f(x) = x²  3x at
the point (2,2). What is the area of the triangle formed by this tangent line and the
coordinate axes?
5.
Find the equation of the tangent line to the curve y  2r³  3x2  3Gx  82 at its point
of inflection
(b) Let y(x) be defined implicitly by the equation 1y  r+ 2y. Find y at the point (2,1).
6.
Find the derivatives of the following functions Simplify your answers
go arctanz
c
In sec r + tan x)
cot:
d)
aresin r + arccos I
(x 1)2
7.
Let /(x) = In(x  1)(x + 1)(x  3)].
What is the domain of the function f(x) ?
For what values of x in the domain of
8
Prove that
9.
b
Show that the equation f(x) = 2x³3x²36x82  0 has a solution for some x* € (4,5).
c
Apply Newton's method to this equation with an initial guess To  4 to find T1 and
evaluate /(I)). Now use To = 5 to find x1 and evaluate f(x1) for this T1. Which one of
these two approximations would you use for x*?
10
Use 'Hopital's rule to find the following limits:
1e2
a
z+0 In(1+1)
lim
tan:
b
linn
=+0 x sin
11
Use the 7 step method to sketch the graph of the curve y = 2r³  3x2  36x  82.
12.
b)
Find a value of c that satisfies the conclusion of the MVT for f(x) = +2  x  6
on
the
interval (1,4).
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