Math 162 Quiz 2 Jan. 26th − 28th, 2016

Please show all your work! Answers without supporting work will not be given credit.Write answers in spaces provided. You have 30 minutes to complete this quiz.

Name:

1. Explain why the slope of the tangent line to the graph of the function at the origin is given by thelimit

limx→0

sinx

x(1)

State if the function is even or odd.

2. Sketch the graphs of the following functions. Make sure to include their domain and to properly labelall points

(a) f(x) = 1− x2

(b) f(x) = x− x2

(c) f(x) = sin(3x)

3. Find the domain of g(t) =√t− 3−

√2 + t

4. Find the limit

limh→0

1(x+h)2 −

1x2

h(2)