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Mathematics 1

Soru

Dakika

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Soru 1

Orta Zorluk

A car moves along a road in such a way that its position at time t is f(t) = t 3 + t 2 + t (metre). What is the average velocity over the interval [1, 5] equal to?

A) 38

B) 38,5

C) 39

D) 39,5

E) 40

Soru 2

Orta Zorluk

If f(x,y)=3x²y+e xy +lny What is the partial derivative ? ² f / ? x² ?

A) y.exy

B) xy.exy

C) 6xy + yexy

D) 6y + y²exy

E) 6x+ exy

Soru 3

Orta Zorluk

Which of the following is the intersection of intervals (-1/3, 4] and [-1, 7/2)?

A) [0, 7/2)

B) [-1, 7/2)

C) [-1, 4)

D) [0, 3)

E) [-1/3, 7/2)

Soru 4

Orta Zorluk

Suppose that demand of a certain product is related to its price by the linear relation q(p)=180-2p, 0≤p≤90. At what price is the elasticity of demand equal to 1?

A) 25

B) 35

C) 45

D) 55

E) 60

Soru 5

Orta Zorluk

A company has a new product which has a demand function, and supply function, What is the market price?

A) 1500

B) 1600

C) 1700

D) 1800

E) 1900

Soru 6

Orta Zorluk

A) 0

B) -66

C) 45

D) -13

E) 14

Soru 7

Orta Zorluk

f (x, y, z) = xyz – xy – xz + yz ; grad f (-1, 2, -3) = ?

A) (-3, -4, -1)

B) (4, 2, 6)

C) (-5, 1, 1)

D) (2, -1, 4)

E) (1, 5, -6)

Soru 8

Orta Zorluk

If f(x) is differentiable on an interval I, I. f '(x) < 0 for all x ? (a, b) then f(x) is called monotone increasing II. f '(x) > 0 is satisfied for all x ? (a, b) then f(x) is called monotone increasing III. f '(x) > 0 is satisfied for all x ? (a, b) then f(x) is called monotone decreasing IV. f '(x) < 0 for all x ? (a, b) then f(x) is called monotone decreasing which of the given statements is true about monotonicity?

A) I and II

B) I and III

C) I and IV

D) I, II and III

E) I, II and IV

Soru 9

Orta Zorluk

Find the lim x›2 (5x-2)(3x²+1).

A) 11

B) 35

C) 72

D) 104

E) 144

Soru 10

Orta Zorluk

Which of the following is the value of lim x›1 (2x³+x-12)/(5x-9)

A) 1/2

B) 0

C) 1

D) 5/2

E) 9/4

Soru 11

Orta Zorluk

Which of the following is the value of ?

A) 0,6

B) 0,36

C) 0,18

D) 0,09

E) 0

Soru 12

Orta Zorluk

Find the gradient of the function f(x,y,z)=xy+zy²+xyz at the point (1,-1,3)?

A) (-2,-2,2)

B) (-4,-2,4)

C) (4,2,1)

D) (-1,1,3)

E) (3,0,-1)

Soru 13

Orta Zorluk

Which one can be said true for derivatives?

A) The derivative of a differentiable function's second derivative can be called the third derivative of the function.

B) The derivative of a differentiable function can be called the second derivative of the function.

C) For the identity function f(x) = x, the derivative is x, that is, (x)' = x.

D) The slope of the secant line to a curve y = f(x) at (x0, f (x0)) is m = f ' (x0).

E) A derivative of a constant is equal to that constant.

Soru 14

Orta Zorluk

A firm faces the demand schedule of D(q)=178-2q, whereas the total cost function is T(q)=q 2 -2q+40. What output will maximize the profit?

A) 20

B) 30

C) 40

D) 50

E) 60

Soru 15

Orta Zorluk

Which one is the infinite representation of 16/20?

A) 1/2

B) 2/3

C) 3/4

D) 4/5

E) 5/6

Soru 16

Orta Zorluk

z = f(x, y) is defined implicitly by xz + yz – 1 = 0 ; ?f / ?x (-1, 2, 1) = ?

A) 1

B) -1

C) 0

D) -2

E) 2

Soru 17

Orta Zorluk

The demand function of A is p = 60 – 3 x / 4, the fixed cost is 120 TL, and the variable cost is 10 TL for each units produced ; which of the following is the profit function ?

A) -0.75 x2– 60

B) -0.75 x2+ 50 x – 180

C) -0.75 x2+ 70 x – 120

D) -0.75 x2+ 50 x – 120

E) -0.75 x2– 50 x – 120

Soru 18

Orta Zorluk

lim x → ∞ (x 3 + x 2 + 1) / (x 4 + x – 1) = ?

A) ∞

B) -∞

C) does not exist

D) 1

E) 0

Soru 19

Orta Zorluk

A particle moves along the x-axis in such a way that its position at time t is . Find the average velocity over the interval [1, 3].

A) 6

B) 7

C) 8

D) 9

E) 11

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