Quiz on Limits and Derivatives

What does the limit of a function f(x) approaching L as x approaches x0 signify?

• f(x) must be a polynomial

• f(x) is always continuous

• f(x) approaches L

• f(x) is defined at x0

What is the Right-Hand Limit?

• Limit considering values of x less than c

• Limit considering values of x greater than c

• Limit at x = c

• Limit at x approaching infinity

When is a limit said to exist?

• When it is a real number

• When it equals infinity

• When it is undefined

• When it is a complex number

What is the average rate of change symbolized as?

• lim ∆x→0 ∆y/∆x

• dy/dx

• ∆y/∆x

• f'(x)

What does continuity in a function imply?

• The function has a limit at every point

• The function can be drawn without lifting the pencil

• The function is always increasing

• The function has no asymptotes

What is the definition of instantaneous rate of change?

• Both b and c

• The derivative at a point

• The limit of the average rate of change as ∆x approaches 0

• The slope of the secant line

What is the notation for the derivative of a function f(x)?

• f'(x)

• f''(x)

• f(x)

• df/dx

What happens if direct substitution in limit calculation yields an undefined value?

• The limit does not exist

• Another method must be used

• The function is continuous

• The limit is infinity

What is the meaning of a discontinuity at point A in a function?

• The function is defined at A

• The graph can be drawn without lifting the pencil

• The limit exists at A

• The graph has a break at A

What is the limit of 1/x^2 as x approaches 0?

• 0

• 1

• +∞

• -∞