Integral Calcul...

 f(x, y) = x²  + xyz + z Find f_x  at (1,1,1)

Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:

The local maximum point of the function f(x) = (x^2/3 ) –x is at  

If x=a(θ+ sin θ) and y=a(1-cos θ), then dy/dx will be equal  

The minimum value of function y = x² in the interval [1, 5] is  

The function f(x) = 2x³ –3x² –36x + 2 has its maxima at  

What should be the value of λsuch that the function defined below is continuous at x = π/22? 

Consider function f(x) =(x² -4)² where x is a real number. Then the function has  

If f      where ai (i = 0 to n) are constants, then   

A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x⁴ –16x³ –24x² + 37 is  

∇×∇×P, where P is a vector, is equal to  

The value of the integral of the function g(x, y) = 4x³ + 10y⁴ along the straight line segment from the point (0, 0) to the point (1, 2) in the x-y plane is  

If     is a differentiable vector function and f is a sufficient differentiable scalar function, then curl   

The temperature field in a body varies according to the equation T(x,y) = x³ +4xy. The direction of fastest variation in temperature at the point (1,0) is given by  

The divergence of vector   

The divergence of the vector  

 Among the following, the pair of vectors orthogonal to each other is  

The directional derivative of the scalar function f(x, y, z) = x² + 2y² + z at the point P = (1,1, 2) in the direction of the vector  

The Gauss divergence theorem relates certain  

If P, Q and R are three points having coordinates (3, –2, –1), (1, 3, 4), (2, 1, –2) in XYZ space, then the distance from point P to plane OQR (O being the origin of the coordinate system) is given by  

Let x and y be two vectors in a 3 dimensional space and denote their dot product. 

Then the determinant det  

If  a  - b  = 3 and  a²  + b²  = 29, find the value of  ab.

If a vector R(t) ^→  has a constant magnitude, then  

For the scalar field    magnitude of the gradient at the point(1,3) is