limits review

LIMITS REVIEW

AP Calculus

Calculate each limit:

li m𝑥→ 0

5 𝑥𝑥

lim𝑥→ 1

𝑥2+5 𝑥+6𝑥+1

lim𝑥→−3

𝑥+1𝑥2+6𝑥+9

Calculate each limit:

li m𝑥→ 2

𝑥3−2 𝑥2+5𝑥−10𝑥−2

If f(x) =

Calculate each limit:

li mh→0

2 (𝑥+h )−5−(2𝑥−5)h

lim𝑥→ 0

sin (2𝑥)𝑥

CALCULATE THE LIMITS IF

lim𝑥→ 2

𝑓 (𝑥)=7𝑎𝑛𝑑 lim𝑥→2

𝑔 (𝑥 )=3

lim𝑥→2

𝑓 (𝑥) ∙𝑔(𝑥)

lim𝑥→ 2

4 𝑓 (𝑥)

lim𝑥→2

𝑔 (𝑥)+2

CALCULATE THE LIMITS

lim𝑥→4−

2𝑥−4

lim𝑥→∞

2𝑥−4

Calculate the limit:

g(x) =

=

Given:

f(x) =

Solve for k such that f is continuous.

Sketch a graph that is discontinuous at x = 3, but approaches a limit of 5 as x approaches 3.

Sketch a function f such that and

Given find the value of x in the interval[4, 7] guaranteed by the Intermediate Value Theoremsuch that y = 10. Round to the nearest thousandth.

INTERMEDIATE VALUE THEOREM

Vertical Asymptotes

Vertical Asymptotes

If h(x) =2limit, L, of h as x approaches 2.

Now find such that if , h is within units of L as x approaches 2.

Epsilon-Delta