Test 1 Review Algebra/Definitions

A collection of flashcards derived from the lecture covering key concepts in algebra and limits.

What is the equation of the tangent line to the curve at a given point?

It is a linear approximation of the function at that point.

What is the definition of the derivative?

The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero.

What does ext{lim }_{x o ext{oo}} [-rac{7}{4x+9}] evaluate to?

The limit evaluates to zero.

What are the vertical asymptotes of the function f(x) = rac{x^2 - 2x}{x^2 - 4}?

Vertical asymptotes occur where the denominator is zero and the function is undefined.

What does it indicate if the left-hand limit and right-hand limit do not match at a certain point?

The limit does not exist at that point.

True or False: The definition of a limit requires that the function be defined at the point 'a' where x approaches.

False.

What is the limit of a function as it approaches a vertical asymptote?

The limit may either approach infinity or negative infinity.

What indicates that a limit evaluates to zero at a point?

The values of the function approach zero as x approaches that point.

What is the algebraic form to find the tangent line at a point on a curve?

It involves using the point-slope form of a line with the derivative at that point.

What is the significance of evaluating limits in calculus?

Limits help determine the behavior of functions near specific points, essential for continuity and differentiability.