Limits Calc

Let f be the function given by f(x)=(x−2)2(x+3) / (x−2)(x+1) . For which of the following values of x is f not continuous?

-1 and 2 only

Question 8 / Your Response What is lim x→∞ x2−4/2+x−4x2

-1/4

If the function f is continuous for all real numbers and if f(x) = x^4 -4 / x +2 when x≠−2, then f(−2)=

-4

limx→0 2x^6+6x^3/ 4x^5 + 3x^3

1/2

Let ff be the piecewise function defined above. The value of limx→2+f(x)limx→2+f(x) is

11

lim n->oo 3n^3-5n / n^3 -2n^2+1

3

If the graph of y=ax+bx+c has a horizontal asymptote y=2 and a vertical asymptote x=-3, then a+c=

5

f(x)={sin(5x)8xcforx≠0forx=0f(x)={sin⁡(5x)8xforx≠0cforx=0 The function ffis defined above, where ccis a constant. For what value of ccis ffcontinuous at x=0

5/8

Question 2 / Your Response Which of the following functions are continuous at x=1 ? I. ln x II. ex III. ln(ex-1)

I, II, and III

The function g is continuous at all x except x=2 If limx→2g(x)=∞which of the following statements about g must be true?

The line x=2 is a vertical asymptote to the graph of g

A polynomial p(x) has a relative maximum at (-2,4) , a relative minimum at (1,1) , a relative maximum at (5, 7) and no other critical points. How many zeros does p(x) have?

Two

limx→7g(x)=6

b

The graph of a function f is shown above. Which of the following limits does not exist?

lim x->5 f(x)

The function f has the properties indicated in the table above. Which of the following must be true?

f is continuous at x=1

For x ≥ 0, the horizontal line y = 2 is an asymptote for the graph of the function f. Which of the following statements must be true?

lim x -> oo f(x) = 2

The graph of a function f is shown in the figure above. Which of the following statements is true?

lim x->a f(x) = 2

The graph of the function h is shown above. What is limx→4h(x)limx→4h(x) ?

nonexistent

The graph of the function f is shown above. For what values of a does limx→a f(x)=0

2 and 4

limx→−3 x2−9/x2−2x−15

3/5