# calculus

What is the limit definition of f'(x) and use it to find f'(x) for f (x) 5x^2 - 2

1. 👍 0
2. 👎 0
3. 👁 94
1. [f(x+h)-f(x)]/h as h-->0

if f(x) = 5 x^2-2
then
f(x+h) = 5(x+h)^2 - 2
5 x^2 + 10 xh + h^2 -2
-5 x^2 -2

= 10 xh +h^2
divide by h
= 10 x + h
take limit as h-->0
= 10 x
done

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Calculus

The area A of the region S that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles. A = lim n → ∞ [f(x1)Δx + f(x2)Δx + . . . + f(xn)Δx] Use this definition to

2. ### Calculus

Hi! My question is: Given that f is a function defined by f(x) = (2x - 2) / (x^2 +x - 2) a) For what values of x is f(x) discontinuous? b) At each point of discontinuity found in part a, determine whether f(x) has a limit and, if

3. ### Calculus

For each sequence an find a number k such that nkan has a finite non-zero limit. (This is of use, because by the limit comparison test the series ∑n=1∞an and ∑n=1∞n−k both converge or both diverge.) D. a_n = (

4. ### CALCULUS help! =)

find the derivative of f(x)=3x^2-x using the limit definition.

1. ### math

Use the limit definition of the derivative to find f′(x) if 1. f(x) = x^2 + 3x 2. f(x) = 1/x + 1 now what i am confuse with is that there is no value given for x. So how is one suppose to do these problems. please show steps and

2. ### Math

For the limit lim x → 3 (x3 − 2x + 5) = 26 illustrate the definition by finding the largest possible values of δ that correspond to ε = 0.2 and ε = 0.1. (Round your answers to four decimal places.)

3. ### Calculus

Find the instantaneous rate of change of V with respect to r when r=100 V(r)=.2r^2-20r+600 using limit definition. Please show work for understanding, thank you :)

4. ### precalcus

can someone explain how to evaluate limits? i only learned how to solve the simpler ones that goes to infinity using the 1/x = 0 or 1/n = 0 rule. am i suppose to make the x whatever number they gave me? but then problem b would be

1. ### math

find derivative using limit definition: f(x) = x - sqrt(x) so f'(x) = lim h->0 [f(x+h) - f(x)]/h but I keep trying to solve by multiplying by the conjugate but I can't figure it out..there's nothing that can be cancelled or

2. ### Math

(a) Find the number c such that the limit below exists. Limit as x goes to -2 of: x^2+cx=c-3/x^2+2x (b) Calculate the limit for the value of c in part (a).

3. ### Limits

Prove using formal definition of limit: Lim 2^(1/n)=1 n->ininity

4. ### Math

limit of (x,y)--->(1,0) of ln(1+y^2/x^2+xy)) Find the limit, if it exists, or show that the limit does not exist.