Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

1. Use the limits definition f' ( x ) = lim (x+h)-f(x) h-0 h to find an expression for the derivative to the functions; a.

image text in transcribed
image text in transcribed
1. Use the limits definition f' ( x ) = lim (x+h)-f(x) h-0 h to find an expression for the derivative to the functions; a. f(x) = 7x b. f(x) = c. f(x) = - 20x3 2. a. Use the limits definition f* ( x ) = lim (xth)-f(x) to find an expression for the derivative to the 1-0 h function y = =x3. b. Using your answer to a) find the slope of the tangent to the curve y = = X to complete the following table. X Slope of tangent (m = y') -3 -2 -1 0 2 3 3. a. After looking closely at the problems and solutions presented in this activity, describe the patterns that you see emerge as you find the derivatives of simple functions like y = x", y = x*, and y = 1/x. (Hint - It might be helpful to remember that, although y = 1/x is written as a rational function, it can also be expressed as a power function. That is, it can be expressed in the form y = x"'). b. Using the patterns that you described in a), find the function that would produce the following derivative of y' = X. 4. a. Find an expression for the instantaneous rate of change of distance with respect to time (velocity) of a falling object if s(t) = -4.91- where s is distance (meters) and t is time (seconds), ignore the effect of air resistance. b. Use your answer for a) to find the velocity at the times listed on the table below. From Physics, you may recall that the velocity is equal to the slope of the distance/time function. Time Velocity (s'(t) = v(t)) 10 sec 45 sec 2 min

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

More Books

Students also viewed these Mathematics questions

Question

13. Give four examples of psychological Maginot lines.

Answered: 1 week ago