Mathematics 1

Yanıt Açıklaması:

Yanıt Açıklaması: E p = |(p / q) (dq / dp)| = 1 for unit elastic ; dq / dp = -0.04 p ; Ep = |(p / (600 – (0.02 p 2 ))) (-0.04 p)| = 1 ; p / (600 – (0.02 p2)) (-0.04 p) = 1 ; 0.04 p 2 / (600 – 0.02 p 2 ) = 1 ; 0.06 p 2 = 600 ; p 2 = 10.000 ; p = 100 . pg. 166. Correct answer is C.

Yanıt Açıklaması: We first find the equilibrium point by equating the supply and demand functions. Therefore, the equality gives Since there will be a shortage in the market, to the left of this point the correct answer is

Yanıt Açıklaması: Writing the demand function for x as x=25-1/4p, and writing the supply as x=2p+20 the equilibrium price may be found as 25-1/4p=2p+20 which is written as 25-20=2p+1/4p and the price is found as p=20/9. Therefore, the answer is D.

Yanıt Açıklaması: If demand is of unit elasticity, i.e. |E p |=1, revenue is unaffected by a small change in price.

Yanıt Açıklaması: If we denote the slope of the curve with m, then:

Yanıt Açıklaması: f(x)=e 3x f'(x)=3e 3x f(x)=9e 3x

Yanıt Açıklaması: We can find the shortest distance by drawing. So the distance between points A and B is √ 2

Yanıt Açıklaması: We first find the equilibrium point by equating the supply and demand functions. Therefore, the equality -4x+150=6x-275, x=42,5. Because there will be a shortage in the market, to the left of this point the correct is x<42,5. Therefore, the answer is B.

Yanıt Açıklaması: velocity at time t=lim h › 0 (f(t+h)-f(t))/h since f ( t ) = 2 t 2 – t : lim h › 0 (f(t+h)-f(t))/h=((2(t+h) 2 -(t+h))-(2t 2 -t))/h =lim h › 0 (2t 2 +2h 2 +4th-t-h-2t 2 +t)/h =lim h › 0 (2h 2 +4th-h)/h =h(2h+4t-1)/h =2h+4t-1 And for t=3 and h=0; 2h+4t-1=11

Yanıt Açıklaması: Since P(x)=R(x)-C(x), according to the given information we can write P(x)=(150-2x)x-(120+60x-x 2 )=-x 2 +90x-120. Now, since there is an extra of 4 TL tax the modified profit function is P(x)=-x 2 +(90-4)x-120=-x 2 +86x-120. The price that maximizes the profit is where the derivative is zero, i.e., P' (x)=-2x+86=0 which is x=43 TL. We insert this value in the price so that p(43)=150-2·43=64 TL.

Yanıt Açıklaması:

Yanıt Açıklaması: The price of a product at the intersection point, provided that it is in the first quadrant, is called market price. Equate the supply and demand function giving; x is found as 30. When we put it on the demand or supply equation, we find market price as 135.

Yanıt Açıklaması:

Yanıt Açıklaması: f(x)=x 2 +lnx-1 f'(x)=2x+(1/x) f''(x)=2-(1/x 2 )

Yanıt Açıklaması: If we substitute x=0 and y=0 the result is 0/0 which is undefined. So we will arbitrarirly take y=kx. Then: (x 2 +3y 2 )/(x 2 -3y 2 )=(x 2 +3k 2 x 2 )/(x 2 -3k 2 x 2 )=x 2 (1+3k 2 )/x 2 (1-3k 2 )=(1+3k 2 )/(1-3k 2 ) The result depends on the value of k. For instance if k=2 result is -13/11, but if k=4 result is -49/47. Therefore the limit does not exit.