Question

The derivative of a function, f(x) is equal to lim h->0 f(x+h)-f(x) / h. True or...

The derivative of a function, f(x) is equal to lim h->0 f(x+h)-f(x) / h. True or false. please explain.

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

The definition is True.

Let's try to understand the limit definition of a derivative.

A derivative is defined as the change of y in a function with respect to a change in x. (in simple words)

Considering the fact that function is differentiable, it must be continuous. Let's consider a continuos function like this:I tried making this image to help you understand it better. Thanks!

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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
Suppose that f : R → R such that, the lim h→0 [f(x) − f(x −...
Suppose that f : R → R such that, the lim h→0 [f(x) − f(x − h)] = 0 for all x ∈ R, then is f continuous in this case?
consider the function f(x)= -1/x, 3, √x+2 if x<0 if 0≤x<1 if x≥1 a)Evaluate lim,→./ f(x)...
consider the function f(x)= -1/x, 3, √x+2 if x<0 if 0≤x<1 if x≥1 a)Evaluate lim,→./ f(x) and lim,→.2 f(x) b. Does lim,→. f(x) exist? Explain. c. Is f(x) continuous at x = 1? Explain.
find the derivative using a definition of the derivative (h) of the following function f(x)= x/(x-1)
find the derivative using a definition of the derivative (h) of the following function f(x)= x/(x-1)
[2 marks] Find the derivative of y  =  √ 4 sin x + 6 at x  ...
[2 marks] Find the derivative of y  =  √ 4 sin x + 6 at x  =  0. Consider the following statements. The limit lim x→0 g(4 + h) − g(4) h is equivalent to: (i) The derivative of g(x) at x  =  h (ii) The derivative of g(x + 4) at x  =  0 (iii) The derivative of g(−x) at x  =  −4 Determine which of the above statements are True (1) or False (2). If  f (3)  = ...
1. Let f(x)=x^2−4x+3/x^2+2X-3   Calculate lim x→1 f(x) by first finding a continuous function which is equal...
1. Let f(x)=x^2−4x+3/x^2+2X-3   Calculate lim x→1 f(x) by first finding a continuous function which is equal to ff everywhere except x=1 . 2. Use the chain rule to find the derivative of the following function 5(−2x^3−9x^8)^12
Given the function h(x)=e^-x^2 Find first derivative f ‘ and second derivative f'' Find the critical...
Given the function h(x)=e^-x^2 Find first derivative f ‘ and second derivative f'' Find the critical Numbers and determine the intervals where h(x) is increasing and decreasing. Find the point of inflection (if it exists) and determine the intervals where h(x) concaves up and concaves down. Find the local Max/Min (including the y-coordinate)
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 =
Consider the function f(x) whose second derivative is f′′(x)=6x+10sin(x). If f(0)=2 and f′(0)=4, what is f(x)?
Consider the function f(x) whose second derivative is f′′(x)=6x+10sin(x). If f(0)=2 and f′(0)=4, what is f(x)?
1. Consider the function f(x) whose second derivative is f″(x)=10x+2sin(x). If f(0)=2 and f′(0)=3, what is...
1. Consider the function f(x) whose second derivative is f″(x)=10x+2sin(x). If f(0)=2 and f′(0)=3, what is f(x)?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT