Homework SourseLet fx1x3 Calculate the difference quotient f2hf2h for h01
Let f(x)=1/(x-3). Calculate the difference quotient (f(-2+h)-f(-2))/h
for:
h=0.1 ____?
h=0.01 ____?
h=-0.01 ____?
h=-0.1 ____?
If someone now told you that the derivative (slope of the tangent line to the graph) of f(x) at x=-2 was -1/n^2 for some integer n what would you expect n to be? ________?
for:
h=0.1 ____?
h=0.01 ____?
h=-0.01 ____?
h=-0.1 ____?
If someone now told you that the derivative (slope of the tangent line to the graph) of f(x) at x=-2 was -1/n^2 for some integer n what would you expect n to be? ________?
Solution
its value be always nearly f\'(-2) = -1/25 = -0.04 for h=0.1 it is (1/-4.9 + 1/5)/.1 = -.0408 for h=0.01 it is (-1/4.99 +1/5)/.01 = -.04008 for h=-.01 it is (-1/5.01 + 1/5)/0.01 = 0.0399 for h=-0.1 it is (-1/5.1 +1/5 )/0.1 = 0.0 392 all are near to 0.04 slope at x=-2 is we have -1/25 so n will be nearly 5
