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Calculus
Y(u)=(u^−2+u^−3)(u^5−1u^2) Find Y′(u)?
Calculus
1) find y'
y = x / (squar root of a^2 - x^2) - shift sin (x-a)
2) use integration by part to verify:
[ Inx / x^2 dx =
3) verify:
[ sin^4 2x dx
y = x / (squar root of a^2 - x^2) - shift sin (x-a)
2) use integration by part to verify:
[ Inx / x^2 dx =
3) verify:
[ sin^4 2x dx
Calculus
1.Any continuous function from the open unit interval (0,1) to itself has a fixed point.
2.logx is uniformly continuous on (1/2,+∞) .
3.If A,B are closed subsets of [0,∞) , then A+B={x+y|x∈A,y∈B} is closed in [0,∞)
4.A bounded continuous function on R is uniformly continuous.
5.Suppose f n (x) is a sequence of continuous functions on the closed interval [0,1] converging to 0 pointwise. Then the integral ∫ 1 0 f n (x)dx converges to 0
2.logx is uniformly continuous on (1/2,+∞) .
3.If A,B are closed subsets of [0,∞) , then A+B={x+y|x∈A,y∈B} is closed in [0,∞)
4.A bounded continuous function on R is uniformly continuous.
5.Suppose f n (x) is a sequence of continuous functions on the closed interval [0,1] converging to 0 pointwise. Then the integral ∫ 1 0 f n (x)dx converges to 0
Calculus
Calculate the mean, variance,skewness and kurtosis for the probability density function with an 'unit' distribution [0,1] (i.e., equal probability of all the values on [0,1])
Calculus
show that the function:
f(x) = { [x-2] [3 + sin(1/x-2)]/[1 + x^2] , if x ≠ 2,
{ 0 , if x = 2.
is continuous at x = 2.
f(x) = { [x-2] [3 + sin(1/x-2)]/[1 + x^2] , if x ≠ 2,
{ 0 , if x = 2.
is continuous at x = 2.
Calculus
(a) Show that the function g(x) =[3 + sin(1/x-2)]/[1 + x^2] is bounded.
This means to find real numbers m; M is an lR such that m ≤ g(x) ≤ M for
all x is an lR (and to show that these inequalities are satis fied!).
(b) Explain why the function:
f(x) = { [x-2] [3 + sin(1/x-2)]/[1 + x^2] , if x ≠ 2,
{ 0 , if x = 2.
is continuous at all x ≠ 2.
(c) Show that the function f(x) in Part (b) is continuous at x = 2. [Hint: Use
Part (a) and the Squeeze Theorem.]
This means to find real numbers m; M is an lR such that m ≤ g(x) ≤ M for
all x is an lR (and to show that these inequalities are satis fied!).
(b) Explain why the function:
f(x) = { [x-2] [3 + sin(1/x-2)]/[1 + x^2] , if x ≠ 2,
{ 0 , if x = 2.
is continuous at all x ≠ 2.
(c) Show that the function f(x) in Part (b) is continuous at x = 2. [Hint: Use
Part (a) and the Squeeze Theorem.]
Calculus
Your startup company Fabulous Fudge Inc. sells to ee lled chocolate
bars that you and your partner manufacture in your parents' garage.
Let p denote the price of one chocolate bar in dollars and q the number of bars. Daily
demand for your chocolate bars is given by:
q(p) = { 1000; if p < 1,
{ 1000(2-p); if 1≤p≤2,
{ 0; if p > 2.
Your production cost is $200 per day plus $0.50 per chocolate bar.
(a) Draw the graphs of your daily revenue R(p) and of your daily cost C(p)
depending on the price p of one chocolate bar.
(b) Determine the break-even points and the interval of prices for which your
business is pro table.
(c) For which price p do you maximize your daily pro fit?
bars that you and your partner manufacture in your parents' garage.
Let p denote the price of one chocolate bar in dollars and q the number of bars. Daily
demand for your chocolate bars is given by:
q(p) = { 1000; if p < 1,
{ 1000(2-p); if 1≤p≤2,
{ 0; if p > 2.
Your production cost is $200 per day plus $0.50 per chocolate bar.
(a) Draw the graphs of your daily revenue R(p) and of your daily cost C(p)
depending on the price p of one chocolate bar.
(b) Determine the break-even points and the interval of prices for which your
business is pro table.
(c) For which price p do you maximize your daily pro fit?
Calculus
(a) Show that the function
g(x) = (3 + sin (1/x-2)/ (1 + x^2)
is bounded. This means to find real numbers m, M E R such that m ≤ g(x) ≤ M for
all x E R (and to show that these inequalities are satisfi ed!).
(b) Explain why the function
f(x) = { [x-2] [3 + sin (1/x-2)/ (1 + x^2)] if x ≠ 2,
{0, if x = 2
is continuous at all x ≠ 2
(c) Show that the function f(x) in Part (b) is continuous at x = 2. [Hint: Use
Part (a) and the Squeeze Theorem.]
g(x) = (3 + sin (1/x-2)/ (1 + x^2)
is bounded. This means to find real numbers m, M E R such that m ≤ g(x) ≤ M for
all x E R (and to show that these inequalities are satisfi ed!).
(b) Explain why the function
f(x) = { [x-2] [3 + sin (1/x-2)/ (1 + x^2)] if x ≠ 2,
{0, if x = 2
is continuous at all x ≠ 2
(c) Show that the function f(x) in Part (b) is continuous at x = 2. [Hint: Use
Part (a) and the Squeeze Theorem.]
Calculus
Suppose 2a + 5b = 10 for some nonnegative real numbers a and b. What is the largest number that the arithmetic mean of a and b can be? (You may want to use some of the techniques from Calc I.)
Calculus
is it possible to have a function whose derivative exists at all the points in domain and there exists a point in the domain at which the derivative of function is discontinuous?if possible give the example of that function in the form of graph
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#339914 on Dec 2023
#339914 on Dec 2023