Graph showing limits approaching from both sides.

$$\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x)$$

Indeterminate form $$\frac{0}{0}$$ or $$\frac{\infty}{\infty}$$ .

$$\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f$$

Condition for differentiability at a point.

f(x) is continuous at x = a and $$\lim_{x \to a} f$$ = $$\lim_{x \to a^+} f$$

Definition of the derivative.

$$\lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$$

Alternative forms for derivatives.

$$\lim_{x \to a} \frac{f(x) - f(a)}{x - a}$$ or $$\lim_{h \to 0} \frac{f(a + h) - f(a)}{h}$$

Derivative of a constant times a function

$$\frac{d}{dx}(c \cdot f(x)) = c \cdot f$$

$$\frac{d}{dx}(f(x) \cdot g(x)) = f$$

$$\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right) = \frac{f$$

$$\frac{d}{dx}(\sin x) = \cos x$$

$$\frac{d}{dx}(\cos x) = -\sin x$$

Derivative of tangent

$$\frac{d}{dx}(\tan x) = \sec^2 x$$

Derivative of cotangent

$$\frac{d}{dx}(\cot x) = -\csc^2 x$$

$$\frac{d}{dx}(\sec x) = \sec x \cdot \tan x$$

Derivative of cosecant

$$\frac{d}{dx}(\csc x) = -\csc x \cdot \cot x$$

Derivative of a Constant Times a Function

Derivatives of inverse cofunctions (arccos x, arccot x, arccsc x)

$$-\frac{1}{\sqrt{1-x^2}}$$ , $$-\frac{1}{1+x^2}$$ , $$-\frac{1}{|x|\sqrt{x^2-1}}$$

Derivatives of inverse functions

Let $$g(x) = f^{-1}(x)$$ . What is $$g$$ ? $$\frac{1}{f$$

$$\frac{d}{dx} (|x|)$$

$$\frac{x}{|x|}$$ for $$x \neq 0$$

Implicit differentiation

Differentiating both sides of an equation with respect to x and solving for $$\frac{dy}{dx}$$

AP Calc Basics Flashcards

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96 questions

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1.

FLASHCARD QUESTION

Front

Back

Limits, Continuity, Differentiability

2.

FLASHCARD QUESTION

Front

Back

Limits, Continuity, Differentiability

3.

FLASHCARD QUESTION

Front

Back

Limits, Continuity, Differentiability

4.

FLASHCARD QUESTION

Front

$f(x)$ is continuous at $x = a$ if

Back

Limits, Continuity, Differentiability

5.

FLASHCARD QUESTION

Front

$f(x)$ is differentiable at $x = a$ if

Back

Limits, Continuity, Differentiability

6.

FLASHCARD QUESTION

Front

L'hôpital's Rule

Back

Limits, Continuity, Differentiability

7.

FLASHCARD QUESTION

Front

Limit definition of $f'(a)$ (Derivative at the point $x = a$)

Back

Derivatives

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