Evaluating Limits and Limit Laws in Calculus

What is the primary reason calculus discusses limits?

• To replace old mathematical frameworks

• To calculate the exact area under a curve

• To understand the behavior of functions as they approach infinity

• To simplify complex equations

What happens to the value of a continuous function as x approaches a specific point?

• It becomes undefined

• It approaches the function's value at that point

• It decreases to zero

• It increases to infinity

How do limits apply to functions with vertical asymptotes?

• Limits are not applicable to such functions

• Limits help in defining the function at the asymptote

• Limits describe the function's behavior as it approaches the asymptote

• Limits simplify the function to avoid the asymptote

What does the limit of a function as x approaches a value indicate when there's a point discontinuity?

• The slope of the function at that point

• The function's behavior as it approaches that point

• The function's maximum value

• The function's value at that point

What is the limit of the function (x minus one) over (x squared minus one) as x approaches one?

• One half

• Zero

• One

• Undefined

What is the limit of sine of x over x as x approaches zero?

• Undefined

• Zero

• One

• Infinity

How do one-sided limits differ from regular limits?

• They simplify the function before calculating the limit

• They are always equal to zero

• They consider the function's behavior from only one direction

• They only apply to continuous functions

What is the limit of a sum of two functions as x approaches a value?

• Undefined

• The product of the limits of each function

• The sum of the limits of each function

• The difference between the limits of each function

What does the limit of a constant times a function equal?

• The constant

• The function's limit

• Zero

• The constant times the function's limit

How can the limit laws be applied to find the limit of a complex function?

• By algebraically manipulating the function according to the limit laws

• By ignoring discontinuities

• By evaluating the function at the limit point

• By graphing the function