Approximating Arc Length or Surface Area In Exercises 65-68, write the definite integral for finding the indicated arc length or surface area. Then use the
Bulb Design An ornamental light bulb is designed by revolving the graph of
about the x-axis, where x and y are measured in feet (see figure). Find the surface area of the bulb and use the result to approximate the amount of glass needed to make the bulb. Assume that the thickness of the glass is 0.015 inch.
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EBK CALCULUS: EARLY TRANSCENDENTAL FUNC
- Find the (exact) direction cosines and (rounded to 1 decimal place) direction angles of = (3,7,6)arrow_forwardLet a = (-1, -2, -3) and 6 = (-4, 0, 1). Find the component of b onto a.arrow_forwardForces of 9 pounds and 15 pounds act on each other with an angle of 72°. The magnitude of the resultant force The resultant force has an angle of pounds. * with the 9 pound force. The resultant force has an angle of with the 15 pound force. It is best to calculate each angle separately and check by seeing if they add to 72°.arrow_forward
- = Let (6,2,-5) and = (5,4, -6). Compute the following: บี.บี. บี. นี = 2 −4(u. v) = (-4). v= ū. (-40) (ū. v) v =arrow_forwardLet ā-6+4j- 1k and b = 7i8j+3k. Find a. b.arrow_forwardFind the volume of the parallelepiped determined by the vectors a = (3, 5, −1), ☎ = (0, 3, 1), c = (2,4,1).arrow_forward
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- Let a = (4, -2, -7) and 6 = (2,5, 3). (ã − ò) × (ã + b) =arrow_forwardUse the graph of the function y = f (x) to find the value, if possible. f(x) 8 7 6 Q5 y 3 2 1 x -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -1 -2 -3 -4 -5 -6 -7 -8+ Olim f(z) x-1+ O Limit does not exist.arrow_forwardIf h(x) = -2x-8 49x2-9 what is lim h(x)? x--00arrow_forward
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