SECTION A: [Short answer questions] 2[ - marks for each question]
QUESTION 1 [25]
1.1. Suppose that lim, f(x) = 12, lim, g(x) = —3.
x=
xXxo--
1.1.1. lim (/3f(+ %g()x) =
Xxo-
1.1.2. li® m ((g(X))° 2 +x) =————---—
Then find
1.1.3. lim (=e) 7
x2-2\\ f(x)
1.1.4. lim (2x + (f(9))?). = se
1.2. Determine the following derivatives.
1.2.1. 2 (sin (:)) inne
1.2.2, a= (e°S*) = COSX) — ___e
1.2.3. If y == In(sinIn(<j x), then a| ss
ee
1.3. Suppose that f and g are continuous functions such that g (4) = 2
and lim (2f(x) + 3g(x)) = 20. Then the value of f (4) = ----------------------
x-
1.4. The domain of the function f(x) = V4 — 9x? is equal to ---------------------
1.5.
lim
fS(ux)pp=os-e-—--a --f-u-n—c-t-i-o-—n
f has
the
property
that
for
all
real
numbers
x,
1-x?
<
f(x)
<
cosx.
Then
x70
SECTION B [Workout Problems]
QUESTION 2 [75]
2.1. Let f(x) = V2+x2. Then
2.1.1. find a formula for f~ +(x).
[5]
2.1.2. state the range of f~1.
[2]
2.2. Evaluate the following limits if it exists.
9394. lim =4 A2
[4]
x9—0o X24+2x341
2.2.2. lim Bet+3 2)
[6]
x2-1 Xt1