Back{Use of Tech} Computing limits with angles in degrees Suppose your graphing calculator has two functions, one called sin x, which calculates the sine of x when x is in radians, and the other called s(x), which calculates the sine of x when x is in degrees.
b. Evaluate lim x→0 s(x) / x. Verify your answer by estimating the limit on your calculator.
Finding Limits
In Exercises 25–28, find the limit of g(x) as x approaches the indicated value.
lim (4g(x))¹/³ = 2
x →0
Finding Limits
In Exercises 25–28, find the limit of g(x) as x approaches the indicated value.
5 ―x²
lim ------------- = 0
x → ―2 (√g(x))
Limits and Infinity
Find the limits in Exercises 37–46.
2x² + 3
lim -------------
x→⁻∞ 5x² + 7
Limits and Infinity
Find the limits in Exercises 37–46.
x⁴ + x³
lim -----------------
x→∞ 12x³ + 128
Limits and Infinity
Find the limits in Exercises 37–46.
sin x
lim ------------- ( If you have a grapher, try graphing
x→∞ |x| the function for ―5 ≤ x ≤ 5 ) .
Limits and Infinity
Find the limits in Exercises 37–46.
x²/³ + x⁻¹
lim --------------------
x→∞ x²/³ + cos²x
Horizontal and Vertical Asymptotes
Use limits to determine the equations for all horizontal asymptotes.
_____
√x² + 4
c. g(x) = -----------
x
Horizontal and Vertical Asymptotes
Use limits to determine the equations for all horizontal asymptotes.
_________
/ x² + 9
d. y = / -------------
√ 9x² + 1
Horizontal and Vertical Asymptotes
Assume that constants a and b are positive. Find equations for all horizontal and vertical asymptotes for the graph of y = (√ax² + 4) / (x―b) .
Limits and Continuity
Suppose that ƒ(t) and ƒ(t) are defined for all t and that lim t → t₀ ƒ(t) = ―7 and lim (t → t₀) g (t) = 0 . Find the limit as t → t₀ of the following functions.
e. cos (g(t))
Limits and Continuity
Suppose that ƒ(t) and ƒ(t) are defined for all t and that lim t → t₀ ƒ(t) = ―7 and lim (t → t₀) g (t) = 0 . Find the limit as t → t₀ of the following functions.
f. | ƒ(t) |
Limits and Continuity
Suppose that ƒ(t) and ƒ(t) are defined for all t and that lim t → t₀ ƒ(t) = ―7 and lim (t → t₀) g (t) = 0 . Find the limit as t → t₀ of the following functions.
h. 1 / ƒ(t)
Limits and Continuity
Suppose the functions ƒ(x) and g(x) are defined for all x and that lim (x → 0) ƒ(x) = 1/2 and lim (x → 0) g(x) = √2. Find the limits as x → 0 of the following functions.
e. x + ƒ(x)
Limits and Continuity
Suppose the functions ƒ(x) and g(x) are defined for all x and that lim (x → 0) ƒ(x) = 1/2 and lim (x → 0) g(x) = √2. Find the limits as x → 0 of the following functions.
f. [ƒ(x) • cos x ] / x―1