BAS CAL REVIEWER

• Calculus - Refers to the branch of mathematics that deals with the study of change
• Limits, Derivatives, Integrals - The three main concepts of calculus
• Limits - Tells us about the values that a function approaches to an a certain input or certain x-value.
• Taking the limit of a function answers the question “what values does a function approach at a certain value”?

  True
• Limits, unlike evaluating functions, we do not care about the values of the function around a point, but rather, we only care about the value of the function at exactly that certain point?

  False
• What does "L" mean in the limit notation?

  The answer to the limit
• The value that x approaches to

  
• A plus sign in the exponent of "a" will denote a Right-sided limit, while a negative sign in the exponent of "a" will denote a Left-sided limit?

  True
• If the left sided limit equals 3, and the right sided limit equals 3, then the two-sided limit is equal to?

  3
• If the left sided limit equals 2, and the right sided limit equals -2, then the two-sided limit is equal to?

  DNE or Does Not Exist
• If the left sided limit equals to positive infinity, and the right sided limit equals negative infinity, then the two-sided limit is equal to?

  DNE or Does Not Exist
• If the two sided limit exists, and the left side limit is equal to 1, then what is the value of the right side limit?

  1
• Evaluate the limit. 7

  
• What does this limit approach to as x approaches 1 from the right? 3

  
• What is the value of f(2.99)?

  5.99

  
• Evaluate the limit?

  -7

  
• What type of limit is shown in the image?

  Left-sided limit

  
• "Choose your x-values to be close to 3, but just a little more than 3." What type of limit is being described by this statement?

  Right-sided limit
• What is the limit as x approaches negative infinity?

  1

  
• Why does the limit as x approaches infinity is equal to 1?

  Because of the horizontal asymptote at y=1

  
• What is the limit as x approaches positive three from the right side?

  2

  
• What is the limit as x approaches positive three from the left side?

  1

  
• If you were the evaluate the function at x=3, which dot will you look at?

  Shaded

  
• What is the limit as x approaches three?

  DNE or Does Not Exist

  
• evaluate the given limit?

  115

  
• Which statement is correct?

  statement two

  
• where L is the limit of f(x) and M is the limit of g(x)?

  M cannot be equal to 0

  
• Evaluate the given limit?

  1

  
• Evaluate the given limit?

  55

  
• what is the conjugate?

  square root of x-3

  
• a2−b2=(a+b)(a−b) is an important formula to know when evaluating limits. What is this formula called?

  Difference of two squares
• Evaluate the limit?

  1/4

  
• Knowing that the numerators and denominators can be factored, what does this limit evaluate to?

  5/3

  
• What method can be used to solve this limit, knowing that it has radicals on the numerator?

  Radical Conjugates

  
• What do we do when the limit evaluates to 0/0 when you substitute the value that x approaches to?

  Try another way to solve the limit, such as factoring, or using radical conjugates
• Evaluate the limit as t approaches 2?

  4

  
• Evaluate the limit as t approaches negative one from the right side?

  5/2

  
• Refers to the property of a function where a function’s graph can be traced without lifting your pen?

  Continuity
• A function is also said to be continuous at "a" if there are no holes, jumps, breaks, asymptotes, etc. at x = a?

  True
• 1. Three conditions of continuity:f(a) exists
  2. The limit as x approaches a of f(x) exists
  3. The limit and the function value at "a" must be equal to 0. which of the following is false?

  3