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Final Sınavı

Mathematics 1

Soru

Dakika

Görüntülenme

Çözülme

Sınav Ayarları

Cevapları Anında Göster

Her soruyu cevapladığınızda doğru/yanlış bilgisi gösterilir

Cevapları Sınav Sonunda Göster

Tüm soruları cevapladıktan sonra sonuçlar gösterilir

Soru 1

Orta Zorluk

Which one is an irrational number?

A) 0

B) 2

C) 3/4

D) π

E) 0.5

Soru 2

Orta Zorluk

Which of the following is the value of lim x›7 [(x 2 -2x - 35) / (x - 7)]

A) 6

B) 7

C) 12

D) 24

E) 42

Soru 3

Orta Zorluk

The bus company BusAway determines that when a return ticket between Eskişehir and Ankara costs p TL (0

A) 6,5

B) 7

C) 8

D) 10,8

E) 12,8

Soru 4

Orta Zorluk

z = x 2 – y ; x = u 2 v ; y = u 2 + v 2 ; at u = v = -1, ?z / ?u = ?

A) -2

B) 3

C) -1

D) -4

E) 1

Soru 5

Orta Zorluk

lim x →- ∞ (x 4 + x 3 – 1) / (x 5 + x 2 + 1) = ?

A) 1

B) does not exist

C) ∞

D) 0

E) -∞

Soru 6

Orta Zorluk

What is the value of the limit; lim (x,y)›(0,0) (5x²+y²) / (x²+y²)=?

A) -5

B) 0

C) 2

D) 5

E) does not exist.

Soru 7

Orta Zorluk

The total cost of A is C (x) = 2.400 + (2 x 2 - 120 x) / 3 , where x represents the quantity produced. Which of the following is the production quantity that makes the cost minimum ?

A) 30

B) 40

C) 64

D) 80

E) 24

Soru 8

Orta Zorluk

If the total cost function of a product is given by C(x)=4x+750, and the demand is p=10-(2x/4) which of the following is the maximum profit obtained through the sales of this product?

A) 3

B) 6

C) 5

D) 7

E) 9

Soru 9

Orta Zorluk

For the function , find the second derivative

A) 1

B) -1

C) 5e

D) 25e

E) 0

Soru 10

Orta Zorluk

The demand function of A is p = 40 – (x / 2), the fixed cost 48 TL, and the variable cost for each item produced is 4 TL ; what is the maximum profit ?

A) 448

B) 860

C) 600

D) 1.022

E) 1.296

Soru 11

Orta Zorluk

lim x ›-1 5 -1 = ?

A) -1

B) 0

C) 0.2

D) 1

E) -0.2

Soru 12

Orta Zorluk

For the function , find the derivative at the point x=0.

A) 8

B) 9

C) 11

D) e

E) e + 1

Soru 13

Orta Zorluk

A) -2xe-x2

B) e-x2(-2+4x2)

C) ex2(-2+4x2)

D) -e-x2(-2-4x2)

E) 4x e-x2

Soru 14

Orta Zorluk

lim x ›2 (x – x -1 ) (x 2 – 1) = ?

A) 4.5

B) 1.5

C) 2.5

D) 0.5

E) 5.5

Soru 15

Orta Zorluk

f(x, y) = e xy + xy 2 – xy + 2 ; ? 2 f / ?y 2 = ?

A) x exy+ 2 x y – x

B) exy+ 2 x

C) x2exy+ x

D) x exy+ x

E) x2exy+ 2 x

Soru 16

Orta Zorluk

Find the equation of the tangent plane to z = ln ( 2 x + y ) at ( - 1 , 3 ).

A) z=4x+2y-2

B) z=x+2y-3

C) z=2x+y-1

D) z=-2x+2y-3

E) z=3x+y-3

Soru 17

Orta Zorluk

The utility function of a consumer is defined by U(x,y)=x 0.5 y 0.5 who is constrained by the budget 120=2x+4y (He has 120 liras to spend on x and y, whose prices are 2 and 4 liras respectively). What are the amounts of (x,y) that maximizes his utility given that he spends all his budget?

A) (30,20)

B) (30,15)

C) (60,0)

D) (0,30)

E) (40,10)

Soru 18

Orta Zorluk

What is the derivative of f(x)=(3x 2 +5x)/(2x-1)

A) (6x2-6x-5)/(4x2-4x+1)

B) (6x2+6x-5)/(4x2+4x-1)

C) (12x2-6x-5)/(4x2-4x+1)

D) (12x2-4x-5)/(4x2-4x+1)

E) 1/(4x2-4x+1)

Soru 19

Orta Zorluk

If then

A) ∞

B) 0

C) 1

D) -1

E) 2

Soru 20

Orta Zorluk

The function z=f(x, y) is implicitly defined by x 2 y-3y 2 +2zx=0. Find dz/dx

A) -y-2z/x

B) -z-2y/x

C) -x-2z/y

D) -x-2y

E) x+y

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