Ünite Sınavı Soruları

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

For z = x²+xy, and x=u²-v and y=-uv, find the partial derivative ∂z / ∂v at u=2, v=-1.

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

For z = x²+ylnx, and x=u³+v² and y=v, find the partial derivative ∂z / ∂v at u=1, v=-3.

What is the shortest distance from point (3,5) to the x=y line?

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?

What can be the maximum area of a rectengular field whose perimeter is 40 metres?

Given that f(x,y)=(3lnx+1)/(e^-3x) + (y²x²)/(x+y)

What is the value of the partial derivative of ∂f / ∂y at the point (1,2)=?

z = f(x, y) is defined implicitly by xz – yz + 3 = 0 ; Which of the following ones below is the equation of the tangent plane to the graph of z = f (x, y) around the point (1, -2, -1) ?

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

For x→0 and y→0 find lim(x²+3y²)/(x²-3y²).

Given that , what is the value of the partial derivative (2, -2)?

The function z=f(x, y) is implicitly defined by x²y-3y²+2zx=0. Find dz/dx

Find the gradient of the function  at the point (-1, 2, 3)?

Assume that z=x²+xy where x=u²v and y=2uv. What is the partial derivative dz/du for u=1 and v=2?

Find the gradient of the function at the point (1, 2, 3)?

Given that , what is the value of the partial derivative  at the point (2, 1)?

What is the shortest distance between the point P(2, 0) and a line y=3x.

f(x, y) = e^xy + xy² – xy + 2 ; ∂²f / ∂x² = ?