Flashcards on Calculus

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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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