Deneme Sınavı Soruları

z = x² – y ; x = u² v ; y = u² + v² ; at u = v = -1, ∂z / ∂u = ?

lim_x→2 (x – x^-1) (x² – 1) = ?

Which of the following is the value of lim_x→2 (x + 3) (2x - 5)?

For which values of x is the function f(x)=(x²-5x+6)/(x²-9) is discontinuous?

For the function

, find the derivative

at the point x=0.

The demand function of A is p(q) = 515 – (q / 5). What is the price when the demand is of unit elastic ?

Which of the following is the local minimum point of the function f (x, y) = 3 x² + y² - 2 x - 4 y ?

At which (x,y) point is the value of the function

y=f(x)=x²-6x+5 is minimum?

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

Which of the following (x,y) points is not a critical one (either maximum, minimum or saddle point) for the function f(x,y)=x²y²-x²-y²?

The motion of a particle is given by the function f(t) = 2t² – t  Find its velocity at the instant t = 3.

What is the solution of 

Which one of these is the minimum : 1 / 3, 2 / 5, 3 / 6, 3 / 10, 7 / 15 ?

1. Consider the function . For every x₁, x₂  A if x₁ ≠ x₂ implies f(x₁) ≠ f(x₂) then the function f is called one-to-one (or injective).
2. Given a function  if the image is equal to the range, i.e. f (A)=B the function f is called surjective (onto).
3. If a function which is both one-to-one and onto is called a bijection.
4. Constant function and identity function are the concepts related to types of functions. A function assigning each element from its domain a single element in its range is called a constant function.
5. Given A ≠, a function defined on the set A and assigning every element of A to itself is called the identity function.

Which of the statements above regarding to properties and types of functions is/are correct?

Which of the following is the intersection of intervals [-3, 5) and [-2, 0)?

Which one of these is the maximum : 2 / 5, 1 / 4, 3 / 8, 3 / 10, 7 / 16 ?

Let the functions f: R→R, f(x)=2x+7 and g: R→R, g(x)=3x-2, what is the value of (gof)(x)?