Calculus Limits and Continuity

Which line is an asymptote to the graph of f(x) = e²x?

y=0

What is lim (3x³ + 4x) / (5 - 2x⁴) as x approaches infinity?

0

If f(x) = 5x³ - 1, what is lim (f(x) - f(0)) / x³ as x approaches 0?

5

What is lim (θ²) / (1 - cos θ) as θ approaches 0?

2

For which function does the table suggest that the limit as x approaches 0 exists?

f only

If a function f is continuous on [1,4] with f(1)=6 and f(4)=-1, what must be true?

f(c) = 1 for some number c in (1, 4).

What are the equations of the asymptotes of f(x) = x / (x(x² - 9))?

x=-3, x=3, y=0

Find the value of k that makes f(x) = {x²+2 if x ≤ -1, kx+4 if x > -1} continuous.

1

If f is an odd function continuous for all real numbers and lim f(x)=-2 as x approaches infinity, which statements must be true?

I, II, and III

What is lim sin(2x) / tan(3x) as x approaches 0?

2/3

If f(x) = (x³+8) / (x+2) when x ≠ -2, what is f(-2)?

12