FINAL EXAM CALCO #2
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FINAL EXAM CALCO #2
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324 5xdx
x
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62 33 5x x dx26
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f x
' 1 2sin cos , 0 3f x x x f
Find if
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2
3
csc
cot
xdxx
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FIND F’(X)
35 2 5f x x
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F(X) = (X2 – 4)3/(X + 2), FIND F’(X)
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F(X) = (SEC5X)4, FIND F’(X)
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2
dyfind
dx
y x xy
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sin 1
dyfind
dxx y y
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A LAMP HANGS 20 FT DIRECTLY ABOVE A STREET ON WHICH A BOY 5 FT TALL IS WALKING. IF THE BOY IS WALKING AWAY FROM THE LIGHT AT THE FATE OF 3 FT/SEC, HOW FAST IS THE BOY’S SHADOW LENGTHENING?
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A man standing on the top of a 128 foot building and throws a ball straight up in the air at a rate of 96 feet per second.
What is the highest point the ball will reach? What is the speed of the ball the instant that it hits the ground?
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THE LENGTH OF A RECTANGLE IS DECREASING AT A RATE OF 2 CM/SEC AND THE WIDTH IS INCREASING AT A RATE OF 2 CM/SEC. FIND THE RATE OF CHANGE OF THE AREA WHEN THE LENGTH OF THE RECTANGLE IS 12 CM AND THE WIDTH IS 5 CM.
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FROM THE EDGE OF A DOCK 12 FEET ABOVE THE SURFACE OF THE WATER, A ROWBOAT IS BEING HAULED IN BY A ROPE AT THE RATE OF 4 FT/SEC. HOW FAST IS THE LENGTH OF THE ROPE CHANGING WHEN THE BOAT IS 5 FEET FROM THE DOCK?
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A SPHERICAL BALLOON IS LOSING HELIUM AT THE RATE OF 12ΠM3/MIN. FIND THE RATE AT WHICH THE SURFACE AREA IS CHANGING AT THE INSTANT THE BALLOON HAS A RADIUS OF 20M.
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FIND THE INTERVALS ON WHICH THE FUNCTION IS INCREASING.
3 2( ) 4 6f x x x
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A CURVE WHOSE SLOPE IS
PASSES THROUGH THE POINT (3, 1). FIND THE COORDINATES OF THE ONLY POINT OF INFLECTION FOR THE GRAPH OF THE CURVE.
2 4x x
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F(X) = SECX, FIND F’’(X)
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