Understanding Limits and Continuity

This video tutorial covers the concept of limits, including graphical and analytical methods for finding limits, one-sided limits, and limits at infinity. It discusses continuity and types of discontinuities, such as jump and point discontinuities. The video also explores special techniques like the squeeze theorem and evaluates limits involving trigonometric functions and infinity.

What is the limit of a function as x approaches -3 from the left if the y-value approaches 2?

• The limit is -3

• The limit does not exist

• The limit is 3

• The limit is 2

Tags

CCSS.HSF-IF.C.7D

Which type of discontinuity is characterized by a sudden jump in the graph?

• Removable discontinuity

• Jump discontinuity

• Infinite discontinuity

• Point discontinuity

When evaluating the limit of a function algebraically, what should you do if direct substitution results in an indeterminate form?

• Use a calculator

• Factor the expression

• Ignore the problem

• Try a different value for x

What is the result of multiplying the top and bottom of a fraction by the conjugate when dealing with radicals?

• The limit does not exist

• The radicals are eliminated

• The expression is unchanged

• The expression becomes more complex

Tags

CCSS.HSF.IF.A.2

What is the y-value of the piecewise function f(x) at x = -3 if f(x) = 2x + 1 for x < -3 and f(x) = x^2 - 14 for -3 ≤ x < 4?

• 5

• 9

• 14

• 0

Tags

CCSS.HSF-IF.C.7D

Which type of discontinuity occurs at x = 4 for the given piecewise function?

• Oscillating discontinuity

• Infinite discontinuity

• Jump discontinuity

• Removable discontinuity

What is the greatest integer less than or equal to 3.9?

• 5

• 4

• 3

• 2

What is the limit of sin(x)/x as x approaches zero?

• 1

• Does not exist

• 0

• Infinity

When analyzing the limit of a natural log function as x approaches zero from the left, what can be concluded?

• The limit is negative infinity

• The limit is positive infinity

• The limit is zero

• The limit does not exist

Which theorem is used to find the limit of x^2 * sin(1/x) as x approaches zero?

• Fundamental Theorem of Calculus

• Squeeze Theorem

• Intermediate Value Theorem

• Mean Value Theorem