Let f(x) =
Find f'(a)
By using the limit definition of the derivative, algebra and limit laws
Let f(x) = Find f'(a) By using the limit definition of the derivative, algebra and limit...
Let f(x) = (4x + 1)2 . Using the limit definition of a derivative f'(a) = limh→0 f(a + h) − f(a) /h find f'(0)
Let f(x) = 3x3 - 24 - 1 Use the limit definition of the derivative to calculate the derivative of f: f'(x) = Use the same formula from above to calculate the derivative of this new function (i.e. the second derivative of f): f''(x) =
3. (5 pts each) Let f(x) = V.. a) Use the limit definition of derivative to find f'(x). b) Use linear approximation to estimate 19.03.
(a) Let f(x) = 3x – 2. Show that f'(x) = 3 using the definition of the derivative as a limit (Definition 21.1.2). 1 (b) Let g(x) = ? . Show that y that -1 g'(x) = (x - 2)2 using the definition of the derivative as a limit (Definition 21.1.2).
For the function f(x)= 5x-1 , Use the limit definition of the derivative to find f (2) Note: You should first use find the derivation of the function; then replace x by 2 in the final answer.
Let f(2) V4.1 +3. f(0) - f(a) Using the definition of derivative at a point, f'(a) = lim enter the expression needed to find the derivative at = 1. > - a f'(1) = lim 11 After evaluating this limit, we see that f'(1) = Finally, the equation of the tangent line to f(x) where x = 1 is Enter here (using math notation or by attaching in an image) an explanation of your solution. Edit - Insert Formats BI...
5. Use the limit definition to find the derivative of f(x) = V3x + 2. (6 points) 6. Find the derivatives of the following functions. Do not simplify after taking the derivative. 5 points each a. f(x) = (4x2 +1) c. h(x) = arcsin(3x2+ 2x-1) b. h(x) = 3sec(x2)
2. Given f(x) = find the derivative using the definition of derivative. 3. Find A and B given that the function, f(x), is continuous at x = 6. V | f(x) = {B (Ar - 42 > 6 4. Find the slope of the tangent line to the curve 2.2 - 2xy + 3y2 = 10 at the point (1,2).
Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x2 + x - 1 the definition of the derivative f'(x) = lim f(x+h)-f(x) h h-0 What is the slope of tangent line to this curve at x = -1?
3. Let f(x) = (a) (15pts) Use the definition of the derivative to find f'(5). (b) (5pts) Write the equation of the tangent line at (5,3).