How do you rewrite the function $$(x^2 - 1)^2$$ for differentiation?

You can rewrite it as $$(x^2 - 1)^{2}$$ to apply the chain rule.

What is the derivative of $$\frac{1}{2}(x^2 - 1)^{-\frac{1}{2}}$$ ?

The derivative is $$-\frac{1}{4}(x^2 - 1)^{-\frac{3}{2}} \times 2x = -\frac{x}{2(x^2 - 1)^{\frac{3}{2}}}$$ .

What is the definition of a limit in calculus?

A limit is the value that a function approaches as the input approaches a certain value.

What is the derivative of $$x^3$$ ?

The derivative of $$x^3$$ is $$3x^2$$ .

What is the power rule in differentiation?

The power rule states that if f(x) = $$x^n$$ , then f'(x) = $$nx^{n-1}$$ .

What is the formula for the surface area of a sphere?

The formula for the surface area of a sphere is $$A = 4\pi r^2$$ , where r is the radius.

What is the definition of continuity at a point?

A function is continuous at a point if the limit as x approaches that point equals the function's value at that point.

What is the quotient rule in differentiation?

The quotient rule states that if you have two functions u(x) and v(x), the derivative of their quotient is given by: $$\frac{(u/v)$$ .

What is the integral of $$x^2$$ ?

The integral of $$x^2$$ is $$\frac{x^3}{3} + C$$ , where C is the constant of integration.

What is the definition of an asymptote?

An asymptote is a line that a graph approaches but never touches or crosses.

Warm up (10/24/19) Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the formula for the VOLUME of a CONE?

Back

2.

FLASHCARD QUESTION

Front

What is the product rule in differentiation?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is the chain rule in differentiation?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the formula for the area of a circle?

Back

7.

FLASHCARD QUESTION

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input has exactly one output.

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