Chapter 2: Q. 34 (page 233)
Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebra.
Short Answer
The derivative of the given function is:
Chapter 2: Q. 34 (page 233)
Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebra.
The derivative of the given function is:
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Get started for freeA bowling ball dropped from a height of feet will be feet from the ground after seconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:
When the bowling ball hits the ground, with
Taking the limit: We have seen that if f is a smooth function, then This approximation should get better as h gets closer to zero. In fact, in the next section we will define the derivative in terms of such a limit.
.
Use the limit just defined to calculate the exact slope of the tangent line toat
Find the derivative of the absolute value function and piecewise defined function
Use (a) the definition of the derivative and then
(b) the definition of the derivative to find for each function f and value in Exercises 23–38.
26.
Use the definition of the derivative to find for each function in Exercises39-54
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