Quandaries
and Queries 

Ashley Student 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^42x^2x 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
by x^{0.5} + a^{0.5}. This gives
Now if you take the limit as x approaches a you get
Are you sure that the third problem is correct? Penny 

