Given f(x) = 4 / (7x+3), find f'(5), using the limit definition of the derivative f'(a) = lim x->a (f(x)-f(a))/(x-a). f'(5) equals the limit as x -> of the expression. The value of this limit is
Added by Jonathan O.
Close
Step 1
Step 1: Calculate f'(5) using the limit definition of the derivative: f'(5) = lim x->5 (f(x) - f(5)) / (x - 5) f'(5) = lim x->5 (4 - 4) / (7x + 3 - 7(5) + 3) f'(5) = lim x->5 0 / (7x + 3 - 38) f'(5) = lim x->5 0 / (7x - 35) f'(5) = 0 / 0 (indeterminate form) Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 92 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Evaluate lim h->0 (f(2 + h) - f(2)) / h where f(x) = 3x + 5. If the limit does not exist, enter DNE. Limit =
Avinash V.
Given f(x) = x - 1 / 2x^2 - 7x + 5, find f(x) as the limit of x approaches 1
Zhumagali S.
Use the limit definition to find the derivative of the function. $$ f(x)=-5 x $$
Differentiation
The Derivative and the Slope of a Graph
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD