Question

Let f ( x ) = cot ⁡ x for 0 < x < π ....

Let f ( x ) = cot ⁡ x for 0 < x < π .

  • (a) State the range of f and graph it on the interval given above.
  • (b) State the domain and range of g ( x ) = cot − 1 ⁡ x . Graph g ( x ) .
  • (c) State whether the graph increases or decreases on its domain.
  • (d) Find each of the following limits based on the graph of g ( x ):
    i. lim x → ∞ g ( x ) ii. lim x → − ∞ g ( x )
    iii.  lim x → ∞ g ′ ( x ) iv. lim x → − ∞ g ′ ( x )
  • (e) Derive the derivative formula for y = cot − 1 ⁡ x .
  • (f) Use the derivative formula in (e) to confirm your answer to parts (c), (d)iii, and (d)iv

This is Calc 2. Please write your process clear as possible.

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