Math 151 Test 2 Print Name Time: 9, 10, 12

Recall that the slope of the tangent line for $f$ at a point $x=a$ is defined to be MATHMATH

  1. If MATH

    1. Use the definition to find the slope of the tangent line at $x=1.$

    2. Find the tangent line equation at $x=1.$

  2. Consider MATH , interpret it as the slope of the tangent line for a function at a point. You need to identify the function and the point.

  3. If MATH

    1. find MATH by showing your work,

    2. determine if $f$ is continuus at $x=0?$ explain.

    3. sketch the graph of $f.$

  4. If MATHThen use the squeezing principle to find the limit of MATH [Specify two functions when applying the squeezing principle.]

  5. Let MATH

    1. Determine the value $a$ so that the function $f$ is continuous everywhere.

    2. Sketch the function $f$ after you find your answer for the number $a.$

  6. Define a function $f$, whose graph is similar to the function, $\sin x, $ and satisfies ALL the following conditions:

    1. the period of $f$ is $4\pi ,$

    2. the function $f$ has amplitude of $4,$

    3. the function $f$ has a maximum at $(\pi ,6).$

  7. Explain why MATH graphically.