1) What point on the parabola y=5x2 is closest to the point (5,5)?

2) A rectangular flower garden with an area of 66 m^2 is surrounded by a grass border 1 m wide on two sides and a 2 m wide on the other two sides. What dimensions of the garden minimize the combined area of the garden andborders?

(a) The vertical height of the garden that will minimize the total area is __m.

(Type an exactanswer, using radicals asneeded.)

(b) The horizontal width of the garden that will minimize the total area is__ m.

(Type an exactanswer, using radicals asneeded.)

3) f(x)=10-x^2 at a=3; f(2.9)

a. Write the equation of the line that represents the linear approximation to the following function at the given point a.

b. Use the linear approximation to estimate the given quantity.

c. Compute the percent error in theapproximation, 100approximationexact/exact, where the exact value is given by a calculator.

4) Evaluate the following limit. Usel'Hpital's Rule when it is convenient and applicable.

lim as n approaches infinity 1+2+...+n/n^2 (HINT: Use 1+2+...n=n(n+1)/2

5) For the functionf, givenbelow, find the antiderivative F that satisfies F(1)=1.

f(x)=x^7-2x^-3+1