[Solved] Calculus-Homework 2

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Problem 1

Draw the graphs of the following equations in two variables x and y.

  1. −3x + 2y = 2
  2. x = 1
  3. (x + 2)2 = 2(2y + 1)
  4. (x + 2)2 + (y− 3)2 = 6
  5. For each of the examples above, determine whether it is the graph of a function y = f(x). If so, find f(x), its domain, and its range.
  6. For each of the examples above, determine whether it is the graph of a function x = g(y). If so, find g(y), its domain, and its range.

Problem 2

Let f(x) = 2x/2. Find the inverse function of f, denoted f−1, and state domain and range of f and f−1.

Note that f−1 is common symbolic notation for the inverse function. It does, however, not denote the function 1/f(x)!

Problem 3

Compute following limits

  1. a) limx→1x2 + 2x− 2

b)

c)

d)

e)

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[Solved] Calculus-Homework 2
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