Question

Let f (x) = (2x - 1) / (x + 2) . Find f ' (x). First set up the limits and simplify the first one. Using equation (6) from Section 3.1 f ' (x) = lim t->x [ ] (simplify; no complex fraction). Using equation (2) from Section 3.2 f ' (x) = lim h->0 [ ] (do not simplify). f ' (x) = ([ ] x + [ ]) / (x + 2)^[ ]

          Let f (x) = (2x - 1) / (x + 2) .
Find f ' (x). First set up the limits and simplify the first one.
Using equation (6) from Section 3.1
f ' (x) = lim t->x [ ] (simplify; no complex fraction).
Using equation (2) from Section 3.2
f ' (x) = lim h->0 [ ] (do not simplify).
f ' (x) = ([ ] x + [ ]) / (x + 2)^[ ]

$Let f (x) = (2x - 1) / (x + 2) . Find f ' (x). First set up the limits and simplify the first one. Using equation (6) from Section 3.1 f ' (x) = lim t->x [ ] (simplify; no complex fraction). Using equation (2) from Section 3.2 f ' (x) = lim h->0 [ ] (do not simplify). f ' (x) = ([ ] x + [ ]) / (x + 2)^[ ]$

Added by Brenda L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/19/2024

Step 1

We can use the limit definition of the derivative: f'(x) = lim (h->0) [(f(x + h) - f(x))/h] Now, let's find f(x + h): f(x + h) = 2 - (x + h) + 2 = 4 - x - h Now, let's plug this into the limit definition: f'(x) = lim (h->0) [(4 - x - h - (2 - x + 2))/h] Show more…

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Let f (x) = (2x - 1) / (x + 2). Find f '(x). First set up the limits and simplify the first one. Using equation (6) from Section 3.1 f' (x) = lim t->x (simplify; no complex fraction). Using equation (2) from Section 3.2 f' (x) = lim h->0 (do not simplify). f' (x) = [ ]x + [ ] / (x + 2)^[ ]