Finding an Equation of a Tangent Line In exercises 67-74, (a) find in equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results. f ( x ) = 4 − x 2 − ln ( 1 2 x + 1 ) , ( 0 , 4 )
Finding an Equation of a Tangent Line In exercises 67-74, (a) find in equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results. f ( x ) = 4 − x 2 − ln ( 1 2 x + 1 ) , ( 0 , 4 )
Finding an Equation of a Tangent Line In exercises 67-74, (a) find in equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results.
Relativity According to the Theory of Relativity, the length
L of an object is a function of its velocity v with respect to an
observer. For an object whose length at rest is 10 m, the func-
tion is given by
L(v) = 10,/1-
where c is the speed of light (300,000 km/s).
(a) Find L(0.5c), L(0.75c), and L(0.9c).
(b) How does the length of an object change as its velocity
increases?
Find an equation of the tangent line to the graph of the function at the given point, (a) use a graphing utility to graph the function and its tangent line at the point, and (b) use the tangent feature of a graphing utility to confirm your results. Function y = (x − 2)(x2 + 3x) Point (1, −4)
Chapter 3, Differentiation
In Exercises 51- 54, find the slope of the tangent line to the graph of the logarithmic function at the point (1, 0).
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