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Questions and Answers
What is the $n^{th}$ derivative of $y = rac{d^n}{dx^n}( ext{sin }x)$?
What is the $n^{th}$ derivative of $y = rac{d^n}{dx^n}( ext{sin }x)$?
- $(-1)^{n} ext{sin }(x + n rac{ ext{ extpi}}{2})$ (correct)
- $(-1)^{n} ext{cos }(x + n rac{ ext{ extpi}}{2})$
- $ ext{sin } x$
- $ ext{cos } x$
What does $ rac{d^{2} z}{d x^{2}}$ equal when $z = au + bv$ and $y = au - bv$?
What does $ rac{d^{2} z}{d x^{2}}$ equal when $z = au + bv$ and $y = au - bv$?
- $ rac{d^{2} u}{d x^{2}} + rac{d^{2} v}{d x^{2}}$
- $0$
- $2a rac{d^{2} u}{d x^{2}} + 2b rac{d^{2} v}{d x^{2}}$ (correct)
- $ rac{d^{2} y}{d x^{2}}$
What is the result of evaluating $ rac{d^{2} z_{i}}{d x_{i}^{2}}$ where $z_{i} = x_{i}^{2}$?
What is the result of evaluating $ rac{d^{2} z_{i}}{d x_{i}^{2}}$ where $z_{i} = x_{i}^{2}$?
- $0$
- $4 x_{i}$
- $x_{i}$
- $2$ (correct)
What is the integral $ rac{ ext{∫}_{0}^{ rac{ ext{ extpi}}{2}} ext{sin}^2(x) dx}$ equal to?
What is the integral $ rac{ ext{∫}_{0}^{ rac{ ext{ extpi}}{2}} ext{sin}^2(x) dx}$ equal to?
What will be the value of $m$ if $ rac{ ext{∂} V}{ ext{∂} x} (2, -3, 4) = m$ for $V = (x^{2} + y^{2} + z^{2})$?
What will be the value of $m$ if $ rac{ ext{∂} V}{ ext{∂} x} (2, -3, 4) = m$ for $V = (x^{2} + y^{2} + z^{2})$?
Flashcards
What's the characteristic equation of a matrix?
What's the characteristic equation of a matrix?
The characteristic equation of a matrix A is a polynomial equation obtained by setting the determinant of (A - λI) to zero, where λ is an unknown scalar and I is the identity matrix. It's used to find the eigenvalues of the matrix.
What are stationary points of a function?
What are stationary points of a function?
The stationary points of a function, also called critical points, are points in the domain of the function where the derivative is zero or undefined. These points might represent local maxima, minima, or saddle points.
What does it mean for functions to be functionally related?
What does it mean for functions to be functionally related?
A function is functionally related if its independent variables can be expressed as a function of other independent variables. This means the original function can be rewritten in terms of these new variables.
What is the nth derivative of a function?
What is the nth derivative of a function?
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What are partial derivatives?
What are partial derivatives?
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