Question

Let f (x) = (5x − 1 )/(x+ 7) . Find f ' (x). First set...

Let f (x) = (5x − 1 )/(x+ 7) . 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) =

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. Let f(x)=−x^2+13x+4 a.Find the derivative f '(x) b. Find f '(−3) 2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate...
1. Let f(x)=−x^2+13x+4 a.Find the derivative f '(x) b. Find f '(−3) 2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded to 2 decimal places. f '(3)= 3. Let f(x)=(x^3+4x+2)(160−5x) find f ′(x). f '(x)= 4. Find the derivative of the function f(x)=√x−5/x^4 f '(x)= 5. Find the derivative of the function f(x)=2x−5/3x−3 f '(x)= 6. Find the derivative of the function g(x)=(x^4−5x^2+5x+4)(x^3−4x^2−1). You do not have to simplify your answer. g '(x)= 7. Let f(x)=(−x^2+x+3)^5 a. Find the derivative....
Consider the function and the value of a. f(x) = -5/x-1, a=7 (a) Use mtan =...
Consider the function and the value of a. f(x) = -5/x-1, a=7 (a) Use mtan = lim h→0 , f(a + h) − f(a) h to find the slope of the tangent line mtan = f '(a). mtan = (b) Find the equation of the tangent line to f at x = a. (Let x be the independent variable and y be the dependent variable.)
13. Consider f(x)=sqrt x-2 a) Using any of the three limit formulas to find f ′...
13. Consider f(x)=sqrt x-2 a) Using any of the three limit formulas to find f ′ ( a ), what is the slope of the tangent line to f ( x )at x = 18? (6 points execution, 2 points notation) b) Find the equation of the tangent line at x = 18 14. State the derivative. a) d/ d x [ x ^n ] b) d /d x [ cos ⁡ x ] c) d /d x [ csc...
Let f(x)=7x^2+7. Evaluate lim h→0 f(−1+h)−f(−1)/h (If the limit does not exist, enter "DNE".) Limit =
Let f(x)=7x^2+7. Evaluate lim h→0 f(−1+h)−f(−1)/h (If the limit does not exist, enter "DNE".) Limit =
f(x) =x2 -x use f'(x)=lim h->0 f(x+h) - f(x)/h find: 1. f '(x) 2. f '(2)...
f(x) =x2 -x use f'(x)=lim h->0 f(x+h) - f(x)/h find: 1. f '(x) 2. f '(2) 3. Find the equation of a tangent line to the given function at x=2 4. f ' (-3) 5. Find the equation of a tangent line to the given function at x=-3
Consider f(x) = x2 – 8x. Find its derivative using the limit definition of the derivative....
Consider f(x) = x2 – 8x. Find its derivative using the limit definition of the derivative. Simplify all steps.     a. Find f(x + h).   ____________     b. Find f(x + h) – f(x).   ____________     c. Find [f(x + h) – f(x)] ÷ h.   ____________   d. Find lim (hà0) [f(x + h) – f(x)] ÷ h.   ____________     e. Find an equation of the line tangent to the graph of y = x2 – 8x where x = -3. Present your answer...
Consider a function f(x; y) = 2x2y x4 + y2 . (a) Find lim (x;y)!(1;1) f(x;...
Consider a function f(x; y) = 2x2y x4 + y2 . (a) Find lim (x;y)!(1;1) f(x; y). (b) Find an equation of the level curve to f(x; y) that passes through the point (1; 1). (c) Show that f(x; y) has no limits as (x; y) approaches (0; 0).
Find the average rate of change for the following function. f(x)=5x^3-3x^2+7 between x=-3 and x=2 The...
Find the average rate of change for the following function. f(x)=5x^3-3x^2+7 between x=-3 and x=2 The average rate of change for f(x) over the interval -3 to 2 is ___ (Type an integer or a simplified fraction.)
lim x→∞ [ln(8 + x^2) − ln(7 + x)] Find the x-value at which f is...
lim x→∞ [ln(8 + x^2) − ln(7 + x)] Find the x-value at which f is discontinuous and determine whether f is continuous from the right, or from the left, or neither. f(x) = 2 + x2      if x ≤ 0 6 − x      if 0 < x ≤ 6 (x − 6)2      if x > 6 x = _____ a) continuous from the right b) continuous from the left    c) neither
Suppose f(x) = (e2x + 5x − 1)4 measures the position of an object at time...
Suppose f(x) = (e2x + 5x − 1)4 measures the position of an object at time x. Find formulas for velocity v(x) and acceleration a(x). Do not simplify