Yahoo Answers Calculus
ELEMENTARY CALCULUS! Limits. Please help!?
ax^3-cx+7 = equation
a=7 c=21
Find the following limit.
lim h -> 0
f(x+h) – f(x) / h
1. First find the Simplified Difference Quotient (SDQ):
2. Now find the following limit:
lim h->0 SDQ=
This is my first week in Calculus. I have worked forever on these problems and cannot figure it out. I plan to get a math tutor ASAP, but until then.. I have hope with yahoo answers. Thanks guys!
Don’t panic.
For f(x+h) simply replace x with x+h in the equation f(x) = ax^3 – cx +7.
This gives you:
f(x+h) = a*(x+h)^3 -c*(x+h)+7
f(x+h) = a*(x^3 +3x^2*h+3x*h^2+h^3)-cx -ch+7
now f(x+h) – f(x) = a*(x^3 +3x^2*h+3x*h^2+h^3)-cx -ch+7 – ax^3 + cx -7
or
f(x+h)-f(x) = 3ax^2*h+3ax*h^2+a*h^3-ch
Now divide by h
[f(x+h)-f(x)]/h = 3ax^2+3ax*h +ah^2 – c
Now take lim as h->0 = 3ax^2 – c = 21*(x^2-1)
Yahoo! Answers?
