Given a circle with radius r , diameter d , circumference C , and area A . a . Write C as a function of r . b . Write A as a function of r . c . Write r as a function of d . d . Write d as a function of r . e . Write C as a function of d . f . Write A as a function of d . g . Write A as a function of C . h . Write C as a function of A .
Given a circle with radius r , diameter d , circumference C , and area A . a . Write C as a function of r . b . Write A as a function of r . c . Write r as a function of d . d . Write d as a function of r . e . Write C as a function of d . f . Write A as a function of d . g . Write A as a function of C . h . Write C as a function of A .
Solution Summary: The author explains that the required relationship is C(r)=2pi r.
Given a circle with radius r, diameter d, circumference C, and area A.
a
. Write
C
as a function of
r
.
b
. Write
A
as a function of
r
.
c
. Write
r
as a function of
d
.
d
. Write
d
as a function of
r
.
e
. Write
C
as a function of
d
.
f
. Write
A
as a function of
d
.
g
. Write
A
as a function of
C
.
h
. Write
C
as a function of
A
.
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
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RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY