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Flashcards on Calculus
Click on the flashcard to see the answer
What is the fundamental theorem of calculus?
The Fundamental Theorem of Calculus states that differentiation and integration are inverse operations.
What is the limit of (1/x) as x approaches infinity?
The limit of (1/x) as x approaches infinity is zero.
What is the derivative of sin(x)?
The derivative of sin(x) is cos(x).
What is the second derivative of f(x) = x^3?
The second derivative of f(x) = x^3 is 6x.
What is the limit of (x^2 - 4x + 4) / (x - 2) as x approaches 2?
The limit of (x^2 - 4x + 4) / (x - 2) as x approaches 2 is 0.
What is the antiderivative of sin(x)?
The antiderivative of sin(x) is -cos(x) + C, where C is a constant of integration.
What is the limit of (1 - cos(x)) / x as x approaches 0?
The limit of (1 - cos(x)) / x as x approaches 0 is 0.
What is the derivative of e^x?
The derivative of e^x is e^x.
What is the limit of (x^2 - 1) / (x - 1) as x approaches 1?
The limit of (x^2 - 1) / (x - 1) as x approaches 1 is 2.
What is the derivative of f(x) = 5x - 2?
The derivative of f(x) = 5x - 2 is 5.
What is the antiderivative of x^3?
The antiderivative of x^3 is (1/4)x^4 + C, where C is a constant of integration.
What is the limit of (sin(x) / x) as x approaches 0?
The limit of (sin(x) / x) as x approaches 0 is 1.
What is the derivative of f(x) = 2x^4 + 3x^2 + 5?
The derivative of f(x) = 2x^4 + 3x^2 + 5 is 8x^3 + 6x.
What is the limit of (3x^3 - 3x^2 - 9x + 9) / (x - 1) as x approaches 1?
The limit of (3x^3 - 3x^2 - 9x + 9) / (x - 1) as x approaches 1 is 0.
What is the antiderivative of 1 / (x^2 + 1)?
The antiderivative of 1 / (x^2 + 1) is arctan(x) + C, where C is a constant of integration.
What is the derivative of f(x) = sec(x)?
The derivative of f(x) = sec(x) is sec(x)tan(x).
What is the fundamental theorem of calculus?
The Fundamental Theorem of Calculus states that differentiation and integration are inverse operations.
What is the limit of (1/x) as x approaches infinity?
The limit of (1/x) as x approaches infinity is zero.
What is the derivative of sin(x)?
The derivative of sin(x) is cos(x).
What is the second derivative of f(x) = x^3?
The second derivative of f(x) = x^3 is 6x.
What is the limit of (x^2 - 4x + 4) / (x - 2) as x approaches 2?
The limit of (x^2 - 4x + 4) / (x - 2) as x approaches 2 is 0.
What is the antiderivative of sin(x)?
The antiderivative of sin(x) is -cos(x) + C, where C is a constant of integration.
What is the limit of (1 - cos(x)) / x as x approaches 0?
The limit of (1 - cos(x)) / x as x approaches 0 is 0.
What is the derivative of e^x?
The derivative of e^x is e^x.
What is the limit of (x^2 - 1) / (x - 1) as x approaches 1?
The limit of (x^2 - 1) / (x - 1) as x approaches 1 is 2.
What is the derivative of f(x) = 5x - 2?
The derivative of f(x) = 5x - 2 is 5.
What is the antiderivative of x^3?
The antiderivative of x^3 is (1/4)x^4 + C, where C is a constant of integration.
What is the limit of (sin(x) / x) as x approaches 0?
The limit of (sin(x) / x) as x approaches 0 is 1.
What is the derivative of f(x) = 2x^4 + 3x^2 + 5?
The derivative of f(x) = 2x^4 + 3x^2 + 5 is 8x^3 + 6x.
What is the limit of (3x^3 - 3x^2 - 9x + 9) / (x - 1) as x approaches 1?
The limit of (3x^3 - 3x^2 - 9x + 9) / (x - 1) as x approaches 1 is 0.
What is the antiderivative of 1 / (x^2 + 1)?
The antiderivative of 1 / (x^2 + 1) is arctan(x) + C, where C is a constant of integration.
What is the derivative of f(x) = sec(x)?
The derivative of f(x) = sec(x) is sec(x)tan(x).
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