Use the drawing to explain the following theorem.“The total area of a right circular cylinder with base area B and lateral area L is given by
.”
What will be an ideal response?
. But the lateral area is that of a rectangle whose length is the circumference C of a circle and whose altitude has length h. Thus, 
or 
, so 
. Each base is circular with radius length r and so each circle has the area 
.
By substitution, 
.
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Evaluate the integral by changing the order of integration in an appropriate way.
A. 2 sin 2 B. 2(1 - cos 2) C. 2(1 + sin 2) D. 2 cos 2
Use l'Hopital's Rule to evaluate the limit.
A. 1
B. 8
C. 
D. ?
Solve the problem.A lens can be described as the volume generated by rotating the first quadrant area under the curve 
about the y-axis (measurements in cm). Find its centroid.
A. 0.833 cm above the center of the base B. 1.25 cm above the center of the base C. 1.67 cm above the center of the base D. 3.33 cm above the center of the base
Provide an appropriate response.Determine which technique would be the best initial step to verify each of the four identities below. Each of the identities involves a different technique as the initial step. 
= 
1 - 
= cos2 ? 
= 2 cot ? - 5 csc2 ? + tan2 ? - cot2 ? = sec2 ?Which of the following is not one of the four techniques required? I. Rewrite the
expression in terms of sines and cosines. II. Multiply the numerator and denominator of a quotient by the conjugate of the denominator. III. Use a Pythagorean identity. IV. Separate a quotient into one or more quotients. V. Use factoring techniques. A. technique III B. technique II C. technique V D. technique IV