Mathematics 1

Yanıt Açıklaması: The function is a rational function. Since the degree of the numerator is less than the degree of the denominator, the following result is true: . The answer is E.

Yanıt Açıklaması: The answer is D.

Yanıt Açıklaması: Once again price elasticity of demand is The answer is A.

Yanıt Açıklaması: The answer is A.

Yanıt Açıklaması: Let us write the demand function for q q=2700-3p Taking the derivative with respect to p we get dq/dp = -3 The price elasticity of demand is From this equation we can easily write the price for the unit elasticity which is 1=3p/(2700-3p) and the sought for price is p=450. Therefore, the answer is C.

Yanıt Açıklaması: (f ° g)(2) equals to f ( g(2) ). g(2), substituting 2 with x in the g function is -2 +3 = 1. Then, (f ° g)(2) = f (1) = 3 . 1 -7 = 3 - 7 = -4.

Yanıt Açıklaması: Price elasticity of demans is

Yanıt Açıklaması: xy=6050 L(x, y, ? ) = x+2y+ ? ( xy -6050). ? L / ? x =0, ? L/ ? y =0, ? L/ ? ? =0 1+ ? y=0, 2+ ? x=0, xy-6050=0 Hence, ? =-1/y=-2/x x=2y 2y²=6050 y=55, x=110 x+2y=220 m.

Yanıt Açıklaması: The additional cost needed to produce or purchase one more unit of a good or service is called the marginal cost. It corresponds to the derivative of the total cost function C(x).

Yanıt Açıklaması: f ( x ) = (x+1 )( 3-x ) f' ( x ) = (x+1 )'( 3-x )+ (x+1 )( 3-x )' f' ( x ) = ( 3-x )+(-x-1) f' ( x ) = 2-2x f' ( x ) =2-2x=0 › x=1 f ( 1 ) = 4

Yanıt Açıklaması:

Yanıt Açıklaması: It is clear that this function has an inverse. Hence, for finding f -1 (x), we write y = 3x + 5. What we find is x = (5 - y) / 3. Then, f -1 (x) = (5 - y) / 3. Substituting 2 with x, we find 1.

Yanıt Açıklaması: E p = |(p / q) (dq / dp)| = 1 for unit elastic ; q = 2.575 – (5 p) ; dq / dp = -5 ; E p = |(p / (2.575 – (5 p))) (-5)| = 1 ; p / (2.575 – (5 p)) (-5) = 1 ; 5 p / (2.575 – 5 p) = 1 ; 10 p = 2.575 ; p = 257.5 . pg. 166. Correct answer is C.

Yanıt Açıklaması: If the company wants to make a profit of 2500TL then the profit function must be equal to this quantity. In other words, P(x)= 2500 ? 80 x-4400=2500?80 x=6900 so that x=86,25 units.

Yanıt Açıklaması: f(x,y)=(3lnx+1)/(e -3x ) + (y²x²)/(x+y) ? f / ? y = [(2x²y).(x+y)-(x+y).1] / (x+y)² By the way x=1,y=-1 ?f / ?y = [(4).(3)-(3).1] / (3)²=1

Yanıt Açıklaması: Becuase x approaches 3 from the right side x is greater than 3 and for x>3, f is given by the rule . So, the result follows as . The answer is A.

Yanıt Açıklaması: If x 2 -6x + 5 = 0 then the roots are {1, 5} from the formula (see p. 54). Since the left side of 1 and the right side of 5 on the sign table are positive (+), the solution of x 2 -6x + 5 < 0 is the interval (1, 5).

Yanıt Açıklaması: e y + x 2 . pg. 183. Correct answer is D.

Yanıt Açıklaması: The profit function we would like to maximise is P(x)=R(x)-C(x) R(x)=x p(x)=x ·(200-3x)=200x -3x 2 so that P(x)=-2x 2 +120x-75 To find the maximum price, let us take the derivative of P(x) and equate it to zero: P'(x)=-4x+120 = 0 ? x=30

Yanıt Açıklaması: (x – 1) (x 2 + x + 1) / (x – 1) = x 2 + x + 1 = 3 ; x ≠ 1 . pg. 108. Correct answer is D.