8075

Mathematics Calculus Level: Misc Level

Give a summary of continuity and differential calculus, standard trignometric derivatives, and standard inverse trignometric derivatives.


8074

Mathematics Calculus Level: Misc Level

Give a summary of continuity and differential calculus, standard trignometric derivatives, and standard inverse trignometric derivatives.


8058

Mathematics Calculus Level: Misc Level

find the coordinates of any relative extrema, and classify as maxima or minima.


8056

Mathematics Calculus Level: Misc Level

the annual world rate of water use t years after 1960 was approximately 860e to the.04t power cubic kilometers per year.how much water was used between 1970 and 1980?


8055

Mathematics Calculus Level: Misc Level

find all relative extrema for f(x,y)=7x2(squared)-5xy+y2(squared)+x-y, and classify each as a maximum or minimum.


8054

Mathematics Calculus Level: Misc Level

find the volume of the solid bounded by f(x,y)=9-x29squared)-y2(squared) over the region for which 0 is less than or equal to x less than or equal to 2 and 0 is less than or equal to y and is lessthan or equal to 1.


8053

Mathematics Calculus Level: Misc Level

the marginal cost of producing x units of a certain product is C, (x)=6x2 (squared)-4. Find the cost function C(x) if the cost of producing 3 units is $8.


8051

Mathematics Calculus Level: Misc Level

A cylindrical can of radius 5cm and height 12 cm is leaking water at a rate of 4 cm 3 (cubed) per minute. How fast is the height of the water changing when the water level is 3 cm from the bottom of the can.(this is a,,related rates,, problem. Volume of a cylinder is given by V=pie r2(squared)h.)


8048

Mathematics Calculus Level: Misc Level

Consider the function y=f (x)=6x-x2. What is the average value of the portion above the x-axis?First sketch the graph and clearly show the x and y intercepts.


8047

Mathematics Calculus Level: Misc Level

A conical container open to the top is being filled at the rate of 10 ft3/min.The container is 20 feet high with a radius of 6 feet at the top.How rapidly is height of the fluid increasing when the height is 10 feet?

Hint;1; Express the cone,s liquid volume in terms of r and h. Then express r in terms of h using the given dimensions of the cone.That allows you to express the liquid volume in cone as a function of just h, the height of the liquid.

Hint;2;Keep n,in your expressions until the very end-tider.


8046

Mathematics Calculus Level: Misc Level

We have a right triangle with one leg growing and one shrinking.By how much is the hypotenuse growing(or shrinking0 if x is increasing at 6 ft/sec and  y is decreasing at 3 ft/sec when x= 60 ft and y=80 ft?Be sure to indicate if the hypotenuse is growing or shrinking.Be careful with the signs of the derivatives.Yes,you must first find the hypotenuse.


8043

Mathematics Calculus Level: Misc Level

The velocity of a particle is given by v(t)=t/(t2+4)^0.5. Find the distance traveled during the first four seconds.Give the exact result using radicals; then a three-decimal place approximation.


8022

Mathematics Calculus Level: Misc Level

Let f (x)=/x for 1<x <7.Use a Riemann sum withn=6 subintervals and sample points the midpoints of the intervals to estimate the area A between the graph of f and the x-axis. The answer that best describes the estimate is 

a. A=13.478

b.A=15.306

c.A=11.680

d.A =11.693

E.None of the other choices is the required Riemann sum


8021

Mathematics Calculus Level: Misc Level

Estimate the area A between the graph f (x)=/36-x2 for 0<4 and the x-axis using four approximating rectangles and left endpoints.The answer that best describes the estimate is 

a.A=22.08 which is an under estimate of A.

b. A=22.77 which is an over estimate of A.

c.A=22.08 Which is an over estimate of A.

d.A=22.77 which is an under estimate of A.

e.None of the other choices is correct


8020

Mathematics Calculus Level: Misc Level

Let f (x)=x2 and divide the interval [0,1] into four subintervals determined by the subdivision points 0,1/4,1/2,3/4,1. The Riemann sun of f with sample points the right endpoints of the subintervals is 

a.15/16

b.15/32

c.1/3

d.2/3

e.None of the other choices is correct


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