ELEMENTARY CALCULUS! Limits. Please help!?

ax^3-cx+7 = equation





a=7 c=21





Find the following limit.


lim h -%26gt; 0





f(x+h) - f(x) / h





1. First find the Simplified Difference Quotient (SDQ):





2. Now find the following limit:


lim h-%26gt;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!

ELEMENTARY CALCULUS! Limits. Please help!?
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-%26gt;0 = 3ax^2 - c = 21*(x^2-1)