Derivatives Of Multivariable Functions

10 Questions | Total Attempts: 114

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Derivatives Of Multivariable Functions

Are you familiar with the mathematical rule, which wants that when all other variables are held constant, then the partial derivative rules for dealing with coefficients, simple powers of variables, constants, and sums/difference of function remain the same, and are used to determine the function of the slope for each independent variable? This more or less, sums up derivatives and multivariable functions. Take our quiz to see how much you really known about them.


Questions and Answers
  • 1. 
    What's the particularity of the function f(x,y) = x^2(y)/ ((x^4) +( y^2))?
    • A. 

      It is that it approaches "100" along any line through the origin.

    • B. 

      It is that it approaches "1" along any line through the origin.

    • C. 

      It is that it approaches "0" along any line through the origin.

    • D. 

      It is that it approaches "-1" along any line through the origin.

  • 2. 
    What happens when the origin is approached along a parabola y=x^2?
    • A. 

      It has a limit of 0.5

    • B. 

      It has a limit of 1

    • C. 

      It is negative

    • D. 

      It is positive

  • 3. 
    If function "f" is symmetric with regard to x and y, what happens to f(x)?
    • A. 

      F(x) is constant.

    • B. 

      F(x) is continuous.

    • C. 

      F(x) is curved.

    • D. 

      F(x) discontinous

  • 4. 
    What is a partial derivative of a multivariable function?
    • A. 

      It is a derivative with respect to 2 variables, with all other variable held constant.

    • B. 

      It is a derivative with respect to 1 variable, with all other variable equal to 0.

    • C. 

      It is a derivative with respect to 1 variable, with all other variable held constant.

    • D. 

      It is a derivative with respect to 1 variable, with 1 variable held constant.

  • 5. 
    What does the multiple integral expand to?
    • A. 

      To the concept of the integral to function of a distinctive number of variables.

    • B. 

      To the concept of the integral to function of certain variables.

    • C. 

      To the concept of the integral to function of any number of variables.

    • D. 

      To the concept of the integral to function of any number equal to 0.

  • 6. 
    What is a gradient theorem?
    • A. 

      It says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve.

    • B. 

      It says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the function.

    • C. 

      It says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the equation.

    • D. 

      It says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the shape.

  • 7. 
    What definition better fit the Stokes theorem?
    • A. 

      The surface integration of the curl of a vector field over a surface Σ in Euclidena three-space to the line integral of the vector field over its curve.

    • B. 

      The surface integration of the curl of a vector field over a surface Σ in Euclidena three-space to the line integral of the vector field over its origin.

    • C. 

      The surface integration of the curl of a vector field over a surface Σ in Euclidena three-space to the line integral of the vector field over its axis.

    • D. 

      The surface integration of the curl of a vector field over a surface Σ in Euclidena three-space to the line integral of the vector field over its boundary.

  • 8. 
    What is the best definition of the Green's theorem?
    • A. 

      It is known as the 3rd integrand of both sides in the integral in terms of P and Q.

    • B. 

      It is known as the 3rd formula of both sides in the integral in terms of P, Q, and R.

    • C. 

      It is known as the 3rd integral of both sides in the integral in terms of P, Q, and R.

    • D. 

      It is known as the 3rd integrand of both sides in the integral in terms of P, Q, and R.

  • 9. 
    What's the other name for the divergence theorem?
    • A. 

      Gauss Theorem

    • B. 

      Ostrogradsky-Gauss theorem

    • C. 

      Gaul theorem

    • D. 

      Ostro-Gauss theorem

  • 10. 
    How would you define Green's theorem?
    • A. 

      The one that gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C.

    • B. 

      The one that gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by B.

    • C. 

      The one that gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by X.

    • D. 

      The one that gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by A.

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