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Questions and Answers
Which of the following MATLAB commands correctly represent the integral of the function $f(x, y, z) = x^{2}e^{y} - 5z^{2}$ with respect to x?
Which of the following MATLAB commands correctly represent the integral of the function $f(x, y, z) = x^{2}e^{y} - 5z^{2}$ with respect to x?
- integral2(@(x,y) x^2 * exp(y) - 5*z^2, 0, 1, 0, 1)
- int(x^2 * exp(y) - 5*z^2, x) (correct)
- integrate(x^2 * exp(y) - 5*z^2, x)
- integral(@(x) x^2 * exp(y) - 5*z^2, 0, 1) (correct)
The MATLAB command for performing element-wise multiplication on two vectors is .*.
The MATLAB command for performing element-wise multiplication on two vectors is .*.
True (A)
What method is used to solve the system of equations provided in Q.3?
What method is used to solve the system of equations provided in Q.3?
Gauss elimination
In the context of Lagrange's interpolation formula, if the $x$ values are 2, 3, and 4, the corresponding $y$ values are ________.
In the context of Lagrange's interpolation formula, if the $x$ values are 2, 3, and 4, the corresponding $y$ values are ________.
Match the MATLAB operations with their descriptions:
Match the MATLAB operations with their descriptions:
Flashcards
MATLAB Integration
MATLAB Integration
In MATLAB, the int function is used to calculate the integral of a function with respect to a given variable. You provide the function and the variable of integration as arguments.
MATLAB Differentiation
MATLAB Differentiation
MATLAB's diff function calculates the derivative of a function. It takes the function and the order of the derivative (e.g., 2 for second derivative) as arguments.
MATLAB Vector Operations
MATLAB Vector Operations
In MATLAB, you can create vectors using the : operator (e.g., 1:5). Mathematical operations between vectors apply element-wise, meaning each element in one vector is combined with its corresponding element in the other vector.
Gauss Elimination
Gauss Elimination
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Lagrange Interpolation
Lagrange Interpolation
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Study Notes
MATLAB Commands
- Q1: Calculate the integral and second derivative of the function f(x, y, z) = x²ey - 5z² with respect to x and z using MATLAB.
Vector Operations in MATLAB
- Q2: Create two vectors of the same length in MATLAB. Perform operations like addition, subtraction, element-wise multiplication, and element-wise division on these vectors.
Solving Linear Equations with Gauss Elimination
- Q3: Solve the system of linear equations using MATLAB and the Gauss elimination method (without pivoting)
- 2x₁ + 8x₂ + 2x₃ = 14
- x₁ + 6x₂ - x₃ = 13
- 2x₁ - x₂ + 2x₃ = 5
Lagrange's Interpolation Formula
- Q4: Use Lagrange's interpolation formula to evaluate y(2.5) from the provided table.
- X values (x) are 2, 3, 4
- Y values (y) are 1.4142, 1.7321, 2.0
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