tutorial 3a mte 3108

MTE3108

TAJUK : PEMBEZAANTutorial 3A

BAHAGIAN A

1. Cari pembezaan bagi y = (x2 + 2x + 5)6 .

(A) (x + 1)(x2 + 2x + 5)6

(B) 2(x + 1)(x2 + 2x + 5)5

(C) 12(x + 1)(x2 + 2x + 5)5

(D) (x + 1)(x2 + 2x + 5)4

2. Diberi h(x) = (x +1)(x2 - 2) , cari nilai h’ (2) ,

(A) 14

(B) 12

(C) 8

(D) - 6

3. Cari pembezaan peringkat pertama bagi g(x) = 4 sin x - 5 cos x + x .

(A) 4 cos x + 5 sin x

(B) 4 cos x + 5 sin x + 1

(C) 4 cos x – 5 sin x + 1

(D) - 4 cos x + 5 sin x + 1

4. Cari pembezaan peringkat ke dua bagi f(x) = .

(A)

(B)

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(C)

(D) -

5. Cari persamaan garis tangen bagi graf fungsi f(x) = 2 sin x pada x = .

(A) y = x -

(B) 6x – 3y =

(C) 3x – 3y =

(D) 3 x – 3y = - 3

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BAHAGIAN B

1 As a balloon in the shape of a sphere is being blown up, the volume is

increasing at the rate of 4 cubic centimeters per second. At what rate is

the radius increasing when the radius is 1 cm?

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2. By using the definition of derivative, find the derivative with respect to

x of f (x) = 1 - x2 . Hence find the equation of tangent to y = 1 – x2

at the point ( 2, - 3 )

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3. The cost and revenue functions for the production of x units of a certain

commodity are C (x) = 4x + 1400 and

R(x) = 20x -

( a ) Show that the profit function is given by P(x) = 16x – 1400 -

and the two break even points are 100 and 700.

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( b ) Find the marginal profit and determine the production level at

which the profit is maximum.

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4. Diberi , tunjukkan

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5. (a) Cari persamaan tangen T, bagi lengkungan , dan berserenjang dengan garis L iaitu .

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(b) Cari koordinat-koordinat titik di mana T bertemu L.

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