Question

Given that a function F is differentiable.

a | f(a) | f^{1}(a) |

0 | 0 | 2 |

1 | 2 | 4 |

2 | 0 | 4 |

Find 'a' such that lim_{x-->a}(f(x)/2(x−a)) = 2.

Provide with hypothesis and any results used.

Answer #1

If f is a continuous, positive function defined on the interval
(0, 1] such that limx→0+ = ∞ we have seen how to make sense of the
area of the infinite region bounded by the graph of f, the x-axis
and the vertical lines x = 0 and x = 1 with the definition of the
improper integral.
Consider the function f(x) = x sin(1/x) defined on (0, 1] and
note that f is not defined at 0.
• Would...

Prove or give a counterexample: If f is continuous on R and
differentiable on R∖{0} with limx→0 f′(x) = L, then f is
differentiable on R.

If f is a differentiable function such that f ' ( x ) ≥ 8 , find
the largest value of M so that f ( 4 ) ≥ M whenever f ( 2 ) = 3

Sketch the graph of a function f(x) that satisfies all of the
conditions listed below. Be sure to clearly label the axes.
f(x) is continuous and differentiable on its entire domain,
which is (−5,∞)
limx→-5^+ f(x)=∞
limx→∞f(x)=0limx→∞f(x)=0
f(−2)=−4,f′(−2)=0f(−2)=−4,f′(−2)=0
f′′(x)>0f″(x)>0 for −5<x<1−5<x<1
f′′(x)<0f″(x)<0 for x>1x>1

Suppose that f is a differentiable function and define
g(x)=e^(2*f(x)+5x). Suppose that f(-2) = 1 and f ' (-2) = 2. Find g
' (-2).

If f is a differentiable function such that f′(x) = (x^2−
16)*g(x), where g(x)>0 for all x, at which value(s) of x does f
have a local maximum?
1. At both x=-4,4
2. Only at x=-16
3. Only at x=4
4. At both x=-16,16
5. Only at x=-4
6. Only at x=16

The density function of random variable X is given by f(x) = 1/4
, if 0
Find P(x>2)
Find the expected value of X, E(X).
Find variance of X, Var(X).
Let F(X) be cumulative distribution function of X. Find
F(3/2)

Theorem 4 states “If f is differentiable at a, then f is
continuous at a.” Is the converse also true? Specifically, is the
statement “If f is continuous at a, then f is differentiable at a”
also true? Defend your reasoning and/or provide an example or
counterexample (Hint: Can you find a graphical depiction in the
text that shows a continuous function at a point that is not
differentiable at that point?)

Let f(x) be a continuous, everywhere differentiable function.
What kind information does f'(x) provide regarding f(x)?
Let f(x) be a continuous, everywhere differentiable function.
What kind information does f''(x) provide regarding f(x)?
Let f(x) be a continuous, everywhere differentiable function.
What kind information does f''(x) provide regarding f'(x)?
Let h(x) be a continuous function such that h(a) = m and h'(a) =
0. Is there enough evidence to conclude the point (a, m) must be a
maximum or a minimum?...

suppose and are functions that are differentiable at x=0 and
that f(1)=2, f'(1)=-1, g(1)=-2, and g'(1)=3. Find the value of
h'(1).
1) h(x)=f(x) g(x)
2) h(x)=xf(x) / x+g(x)

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 6 minutes ago

asked 7 minutes ago

asked 12 minutes ago

asked 19 minutes ago

asked 19 minutes ago

asked 30 minutes ago

asked 37 minutes ago

asked 38 minutes ago

asked 40 minutes ago

asked 42 minutes ago

asked 1 hour ago