1) Find the average rate of change of the function over the given interval. a) f(x) = x³ + 1, [2,3] b) f(x) = cotx, 2) Use the method in example 2 to find a) the slope of the curve at the given point P and b) find an equation of the tangent line at a) y = x - 3, P(2,1) b) y = x, P(2,8) 3) For the function f(t) graphed here, find the following limits or explain why they do not exist. a) lim f(t) b) lim f(t) lim f(t) d) lim f(t) --1 s = f(t) -1 4) Which of the following statements about the function y = f(x) graphed here are true, and which are false? a) lim f(x) does not exist.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Exercises.2.1and2.2:
1) Find the average rate of change of the function over the given
interval.
a) f(x) = x³ +1, [2,3]
b) f(x) = cotx ,
2) Use the method in example 2 to find a) the slope of the curve at the
given point P and b) find an equation of the tangent line at a
a) y = x - 3, P(2,1)
b) y = x, P(2,8)
3) For the function f(t) graphed here, find the following limits or
explain why they do not exist.
a) lim f(t)
b) lim f(t)
d) lim f(t)
t-2
s- f(t)
-1
4) Which of the following statements about the function y f(x)
graphed here are true, and which are false?
a) lim f(x) does not exist.
b) lim f(x) = 2
c) lim f(x) does not exist.
X-1
Transcribed Image Text:Exercises.2.1and2.2: 1) Find the average rate of change of the function over the given interval. a) f(x) = x³ +1, [2,3] b) f(x) = cotx , 2) Use the method in example 2 to find a) the slope of the curve at the given point P and b) find an equation of the tangent line at a a) y = x - 3, P(2,1) b) y = x, P(2,8) 3) For the function f(t) graphed here, find the following limits or explain why they do not exist. a) lim f(t) b) lim f(t) d) lim f(t) t-2 s- f(t) -1 4) Which of the following statements about the function y f(x) graphed here are true, and which are false? a) lim f(x) does not exist. b) lim f(x) = 2 c) lim f(x) does not exist. X-1
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