Limits of Average Rates of Change Because of their connection with secant lines, tangents, and instanta- neous rates, limits of the form f(x + h) – f(x) lim h→0 h occur frequently in calculus. In Exercises 57–62, evaluate this limit for the given value of x and function f. 57. f(x) = x², x = 1 59. f(x) = 3x – 4, x = 2 61. f(x) = Vx, x = 7

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Limits of Average Rates of Change
Because of their connection with secant lines, tangents, and instanta-
neous rates, limits of the form
f(x + h) – f(x)
lim
occur frequently in calculus. In Exercises 57–62, evaluate this limit
for the given value of x and function f.
57. f(x) = x², x = 1
59. f(x) = 3x – 4, x = 2
61. f(x) = Vx, x = 7
-
Transcribed Image Text:Limits of Average Rates of Change Because of their connection with secant lines, tangents, and instanta- neous rates, limits of the form f(x + h) – f(x) lim occur frequently in calculus. In Exercises 57–62, evaluate this limit for the given value of x and function f. 57. f(x) = x², x = 1 59. f(x) = 3x – 4, x = 2 61. f(x) = Vx, x = 7 -
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