Question

- State (precisely) the limit definition for the derivative of an
arbitrary function f(x) at the point
. Use the limit definition to compute the derivative of the following function: f(x) =*x*_{0}*1/x^2*

Answer #1

Assumptions:
The formal definition of the limit of a function is as follows:
Let ƒ : D →R with x0 being an
accumulation point of D. Then ƒ has a limit L at
x0 if for each ∈ > 0 there is a δ > 0
that if 0 < |x – x0| < δ and
x ∈ D, then |ƒ(x) – L| <
∈.
Let L = 4P + Q. when P = 6 and Q = 24
Define...

Using the derivative definition, point the derivative value for
the given function f(z)=3/z^2 Find in Z0=1+i and write x+iy
algebraically.

Please Find: f(x)=x2+2
1) The derivative of f(x) using the limit definition:
2) The instantaneous rate of change at x=3:
3) The equation of the tangent line at x=3:
Please write out all the steps clearly.

Show that the derivative of f(x) = 6+4x^2 is f' (x)=8x by using
the definition of the derivative as the limit of a difference
quotient.

Use
the limit definition of the derivative to find the equation of the
tangent line to f at x = 3 3 f(x) = 1/(x + 1) Show all of your
work

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...

Find the derivative of the function using the definition of
derivative.
g(x) =
sqrt 9 −
x
g' (x) =
State the domain of the function. (using interval notation.)
State the domain of its derivative. (using interval notation.)

Let f(x)=3x2+10x+3.
a) Find the derivative of f(x) using the definition of the
derivative.
b) Find the equation of the tangent line at point x=−1

use the definition of the derivative to find
f′(3) if f(x) = x^2 - 2x

Use the definition of the derivative to show that f(x) = |x^2 –
9| is not differentiable at x = 3

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