Ünite Sınavı Soruları

lim_{x→0, y→0} (x³ + xy + y²) / (x + xy + y²) = ?

Which of the following functions is not continuous at point (1,2)?

z = x + y² ; x = u - v ; y = u v² ; at u = v = -1, ∂z / ∂v = ?

What is the value of the limit;

lim_{(x,y)→(0,0)}  (5x²+y²) / (x²+y²)=?

What is the partial derivative df(x,y)/dx for f(x,y)=e^xy?

z = f(x, y)= xz + yz + 1  so  ∂f / ∂y (1, -2, -1) = ?

If f(x,y)=x²+5xy-3y² find f_xy-f_yx

What is the second degree partial derivative d²f(x,y)/dxdy for f(x,y)=e^xy?

What is the positive stationary vaule of the function f (x, y) = x – y, satisfying the condition x² – 2 y² = 10 ?

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

What is the limit of the function f(x,y)=(x²-y²)/(5x-5y) for x=1 and y=1?

What is the value of the limit 

What is the shortest distance between the point P(0, -4) and the line y = x ?

If f(x,y)=5+e^-3y+x.lnx

What is the partial derivative ∂f/∂x= ?

What is the positive stationary value of the function f (x, y) = x + 2 y, satisfying the condition 2 x² – y² = -14 ?

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

The utility function of a consumer is defined by U(x,y)=x^0.5y^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?

Which of the following (x,y) points is a local maximum for the function f(x,y)=x²y²-x²-y²?

What is the equations of a normal line for a function f (x, y) = x²+3y² at a point (x, y) = (1, 1)?

f(x, y) = e^y + yx² – x – 1 ; ∂f / ∂x = ?