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Chapter 2 | Limits
2.1 EXERCISES For the following exercises, points P (1, 2) and Q ( x , y ) are on the graph of the function f ( x ) = x 2 +1. 1. [T] Complete the following table with the appropriate values: y -coordinate of Q , thepoint Q ( x , y ), and the slope of the secant line passing through points P and Q . Round your answer to eight significant digits. x y Q ( x , y ) m sec
5. Use the values in the right column of the table in the preceding exercise to guess the value of the slope of the tangent line to f at x =1. 6. Use the value in the preceding exercise to find the equation of the tangent line at point P . Graph f ( x ) and the tangent line. For the following exercises, points P (4, 2) and Q ( x , y ) are on the graph of the function f ( x ) = x . 7. [T] Complete the following table with the appropriate values: y -coordinate of Q , thepoint Q ( x , y ), and the slope of the secant line passing through points P and Q . Round your answer to eight significant digits. x y Q ( x , y ) m sec
1.1
a.
e.
i.
1.01
b.
f.
j.
1.001
c.
g.
k.
4.1
a.
e.
i.
1.0001 d.
h.
l.
4.01
b.
f.
j.
2. Use the values in the right column of the table in the preceding exercise to guess the value of the slope of the line tangent to f at x =1. 3. Use the value in the preceding exercise to find the equation of the tangent line at point P . Graph f ( x ) and the tangent line. For the following exercises, points P (1, 1) and Q ( x , y ) are on the graph of the function f ( x ) = x 3 . 4. [T] Complete the following table with the appropriate values: y -coordinate of Q , thepoint Q ( x , y ), and the slope of the secant line passing through points P and Q . Round your answer to eight significant digits. x y Q ( x , y ) m sec
4.001
c.
g.
k.
4.0001 d.
h.
l.
8. Use the values in the right column of the table in the preceding exercise to guess the value of the slope of the tangent line to f at x =4. 9. Use the value in the preceding exercise to find the equation of the tangent line at point P . For the following exercises, points P (1.5, 0) and Q ⎛ ⎝ ϕ , y ⎞ ⎠
are on the graph of the function f ⎛ ⎝ ϕ ⎞
⎛ ⎝ πϕ
⎞ ⎠ .
⎠ =cos
1.1
a.
e.
i.
1.01
b.
f.
j.
1.001
c.
g.
k.
1.0001 d.
h.
l.
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