MATH026: Limits (Multiple choice)

If the limit of f(x) as x approaches 2 is 5, denoted as limₓ→2 f(x) = 5, what can we conclude?

• f(x) is constant at 5.

• As x gets closer to 2, f(x) gets closer to 5.

• f(x) can never reach 5.

• f(2) must equal 5.

• As x gets closer to 2, f(x) gets closer to 5.

Which limit property states that the limit of a product equals the product of the limits?

• Limit of Quotients Property

• Limit of Sums Property

• Limit of Differences Property

• Limit of Products Property

• Limit of Products Property

What feature of a graph indicates a limit approaching infinity at a certain point?

• A vertical asymptote.

• A maximum point.

• A point of discontinuity.

• A horizontal asymptote.

• A vertical asymptote.

What is the limit of f(x) = 1/x as x approaches 0 from the right?

• Infinity

• Undefined

• 0

• Negative infinity

• Infinity

What is the range of the function f(x) = x²?

• All non-negative real numbers.

• Just the number 0

• All real numbers

• All positive real numbers

• All non-negative real numbers.

Which of the following represents the limit of a function as x approaches a certain value?

• a→f(x)

• f(x) as x→a

• f(a)

• limₓ→a f(x)

• limₓ→a f(x)

If f(x) = x², what is f(3)?

• 3

• 6

• 9

• 12

• 9

Which of the following is a correct statement about continuous functions?

• A continuous function must be linear.

• A continuous function always increases.

• A continuous function has no breaks, jumps, or holes.

• A continuous function must have a limit at every point.

• A continuous function has no breaks, jumps, or holes.

What is the definition of a function?

• A relationship between two variables that represents a change.

• A sequence of numbers that follows a pattern.

• A relation that can assign multiple outputs for each input.

• A relation that assigns exactly one output for each input.

• A relation that assigns exactly one output for each input.

What property of limits states that the limit of a sum is the sum of the limits?

• Limit of Constant Multiples Property

• Limit of Sums Property

• Limit of Quotients Property

• Limit of Products Property

• Limit of Sums Property

Which property of limits states that the limit of a sum is the sum of the limits?

• Limit of a Constant Property

• Limit of a Quotient Property

• Limit of a Product Property

• Limit of a Sum Property

• Limit of a Sum Property

What is the limit of f(x) = 1/x as x approaches 0 from the positive side?

• -∞

• +∞

• 0

• 1

• +∞

What is the limit of the piecewise function f(x) = {x + 2 for x < 1, 3 for x = 1, x^2 for x > 1} as x approaches 1?

• 4

• 3

• 2

• 1

• 3

What does it mean if the limit as x approaches a is infinity?

• The function is undefined at that point.

• The function stays constant at that point.

• The function approaches a finite value.

• The function increases indefinitely as x approaches a.

• The function increases indefinitely as x approaches a.

Using the epsilon-delta definition, what does it mean if the limit of f(x) as x approaches c is L?

• f(x) must equal L at x = c.

• For every ε > 0, there exists a δ > 0 such that if |x - c| < δ, then |f(x) - L| < ε.

• If f(c) = L, then the limit exists.

• The function f(x) is continuous at x = c.

• For every ε > 0, there exists a δ > 0 such that if |x - c| < δ, then |f(x) - L| < ε.

Which of the following statements is true for limits?”

• Limits can only be computed numerically.

• The limit and the function value are always equal.

• The limit of a function does not necessarily equal the function's value at that point.

• If a limit exists, the function must be continuous.

• The limit of a function does not necessarily equal the function's value at that point.

If f(x) is continuous at x = c, what can we say about the limit of f(x) as x approaches c?

• It is undefined.

• It does not exist.

• It equals f(c).

• It equals c.

• It equals f(c).

What does the limit of a function as x approaches a value represent?

• The function value at that point.

• The value that f(x) approaches as x gets closer to that value.

• The instantaneous rate of change of the function.

• The maximum value of the function.

• The value that f(x) approaches as x gets closer to that value.

If limit as x approaches a of f(x) = L and limit as x approaches a of g(x) = M, what is the limit of the product f(x)g(x) as x approaches a?

• 0

• L/M

• LM

• L + M

• LM

Evaluate lim (x → ∞) (1/(x^2)).

• -1

• 0

• 1

• ∞

• 0