Quandaries and Queries


Secondary Question:
Hi, I am having a lot of trouble with three calculus questions and was wondering if you could help...pleaseee
1. Find the two points on the curve y=x^4-2x^2-x that have a common tangent line.
2. If f is differentiable at a, where a>0, evaluate the following limit in terms of f ' (a):
            lim x--> a  f(x)-f(a) / x^ .5 - a^ .5
3. Evaluate:
            lim x--> 0  (sin(3+x)^2 - sin 9) / (x)  
Thanks for all your'e help.


Hi Ashley,

I'll show you how to do the second problem. Multiply the numerator and denominator of

 f(x)-f(a)/x0.5 - a0.5

by x0.5 + a0.5.

This gives

 f(x)-f(a)/x - a (x0.5 + a0.5)

Now if you take the limit as x approaches a you get

2 a0.5 f '(a).

Are you sure that the third problem is correct?



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