AP Calculus AB Quiz 2 mc practice

Let f(x) be defined by the function to the left. For what value(s) of x is f(x) NOT continuous?

• -1 only

• 0 only

• 4 only

• 0 and 4 only

• -1, 0, and 4

Tags

CCSS.HSF-IF.C.7B

Which of the following functions are continuous on the interval 1 < x < 6? (*hint: it means there's no hole or v.a. in that interval)

• II only

• I and II only

• I and III only

• II and III only

Tags

CCSS.HSF-IF.C.7D

The graph of the function g(x) is shown. Which of the following statements about g(x) is true?

• I only

• I and II only

• I and III only

• I, II, and III

• II and III only

• 1

• 0

• dne

• -1

• 1

• 3

• 0

• 0

• 4

• Limit dne

Answer explanation

When your numerator is an expression of more than one term and the denominator is only 1 factor, try to separate the fraction so you can take care of the limit of each fraction. In this case, 12x/3x is one fraction, which you can simplify to 12/3, so the limit for this one is 4. Then the second fraction is sinx/3x, and it's a special limit as x->0, which is 1/3. Then you add 4 + 1/3, get common denominator.. so it's 13/3

• I only

• II only

• III only

• I and II only

• II and III only

Tags

CCSS.HSF-IF.C.8B

Answer explanation

x goes to infinity, so the exponent for 5^x will become bigger positive, so the value of 5^x will become bigger and bigger, so the limit is infinity (unbounded bc it keeps getting bigger)

Tags

CCSS.HSF-IF.C.8B