Calculus Answers

Micros Unlimited corporation (a local distributor of micro computers) sells one of its 586-based system on a volume

discount as follows: 1 to 5 units at a price of $4495 per unit, units 6 through 10 at a price of $ 4095 per unit, and

any unit in excess of 10 at a price of $3775 per unit.

i. Determine the cost function and draw its graph.

ii. What are the total and average cost s of 4 units ?

iii. What are the total and average cost s of 15 units?

iv. How many units were purchased if the total charge was $58,050 ?

v. How many units were purchased if the average charge was $4035?

Find the minimum distance from the point (4, 2) to the parabola y²=8x.

From a thin piece of cardboard 10 in. by 10 in., square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary.

A. 6.7 in. x 6.7 in. x 3.3 in.; 148.1 in³

B. 3.3 in. x 3.3 in. x 3.3 in.; 37 in³

C. 5 in. x 5 in. x 2.5 in.; 62.5 in³

D. 6.7 in. x 6.7 in. x 1.7 in.; 74.1 in³

Find the number of units that must be produced and sold in order to yield the maximum profit, given the following equations for revenue and cost:

R(x) = 30x - 0.5x 2

C(x) = 5x + 7.

A. 32 units

B. 26 units

C. 35 units

D. 25 units

Using the Epsilon and Delta definition, show that lim x approaching 2 for (3x-5) is =1

If f(x) = 2|x-1| and g(x) = 3x-10 , then f o g (1) = 12 .

True or false? Give reason.

Do the domain of the function f defined by √(3-x) /(x-2) is R - {2}

Find the domain and range of the function f defined by f(x) = 1/1-sinx

Find the following limits:

lim x approches 2 for x^2 + 4x -1/ x^2 -2x

Is the function f : R ➡R, defined by f(x) = 1-|x| is differentiable at x=1