A. Use your calculator to approximate ∫^ b_0 e^-0.00001x dx for b=10, 50, 100 and 1000.b. Based on your answers to part a, does ∫^[infinity]_0 e^-0.00001 dx appear to be convergent or divergent?
c. To what value does the integral actually converge?

Answers

Answer 1
Answer:

Answer:

Step-by-step explanation:

We are to integrate the function

e^-0.00001x from 0 to b for different ascending values of x.

\int e^-0.00001x = -10^5 e^-0.00001x

Now we substitute the limits

When b =10

I = integral value = -10^5 e^-0.00001*10

b =50, I = -10^5(e^-0.00001*50-1)

b =100, I = -10^5( e^-0.00001*100-1)

b =1000 I=  -10^5 (e^-0.00001*1000-1)

b) As b increases exponent increases in negative, or denominator increases hence when b becomes large this will be a decreasing sequence hence converges

c) Converges to  -10^5 (0-1)=10^5


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Solve the algebraic expression n + 8, if n = 15

Answers

you mean evaluate

n+8
if n=15
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What is the quotient and remainder of 8 divided 25

Answers

the answer is 3 reminder 1


An experiment is pulling a ball from an urn that contains 3 blue balls and 5 red balls. a.) Find the probability of getting a red ball. b.) Find the probability of getting a blue ball. c.) Find the odds for getting a red ball. d.) Find the odds for getting a blue ball.

Answers

Answer:

Step-by-step explanation:

The urn contains 3blue balls 5 red balls

a) probability of getting a red ball

   P=no of favourable of outcomes /total no outcomes

   P(red ball) = 5/8

b) Probability of blue ball

  P(blue ball) = 3/8

c) Odds getting a red ball

   odds in favour of any object = m/n

   m : event to occur

   n  : event will not occur

 Odds(red ball) = 5/3

d)

Odds(blue) = 3/5

Find the Derivative.
f(x) = -xcos3x

Answers

Answer:

(d)/(dx)(-xcos3x)=  3x \ sin(3x)- cos(3x)

Step-by-step explanation:

Use the Product Rule for derivatives, which states that:

  • (d)/(dx) =[f(x)g(x)]= f(x)g'(x)+f'(x)g(x)

In the function we are given, f(x)=-x \cos3x, we can break it up into two factors: -x is being multiplied by cos3x.

Now, we have the factors:

  • -x \n   $cos 3x

Before using the product rule, let's find the derivative of cos3x using the chain rule and the power rule.

  • (d)/(dx)(cos3x)= (d)/(dx) (cos3x) * (d)/(dx) (3x) \n (d)/(dx)(cos3x)= (-sin3x) * 3 \n (d)/(dx) (cos3x) = -3sin(3x)

Now let's apply the product rule to f(x) = -xcos3x.

  • (d)/(dx)(-xcos3x)=  (-x)(-3sin3x) + (-1)(cos3x)

Simplify this equation.

  • (d)/(dx)(-xcos3x)=  (x)(3sin3x) - (cos3x)

Multiply x and 3 together and remove the parentheses.

  • (d)/(dx)(-xcos3x)=  3x \ sin(3x)- cos(3x)

Therefore, this is the derivative of the function f(x)=-xcos3x.

Hi there!

\large\boxed{f'(x) =  -cos3x + 3xsin3x}

f(x) = -xcox3x\n\n\text{Use the product rule and chain rule to solve for the derivative:}\n\n(dy)/(dx)= -cos3x + (-x * (-sin3x) * 3)\n\n= -cos3x + 3xsin3x

ree heights: Cherry trees in a certain orchard have heights that are normally distributed with mean μ = 119 inches and standard deviation σ = 17 inches. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least four decimal places. (a) What proportion of trees are more than 130 inches tall? (b) What proportion of trees are less than 90 inches tall? (c) What is the probability that a randomly chosen tree is between 95 and 105 inches tall? Part: 0 / 30 of 3 Parts Complete Part 1 of 3 What proportion of trees are more than 130 inches tall? The proportion of trees that are more than 130 inches tall is .

Answers

Answer:

a) 0.2588

b) 0.044015

c) 0.12609

Step-by-step explanation:

Using the TI-84 PLUS calculator

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

From the question, we know that:

μ = 119 inches

standard deviation σ = 17 inches

(a) What proportion of trees are more than 130 inches tall?

x = 130 inches

z = (130-119)/17

= 0.64706

Probabilty value from Z-Table:

P(x<130) = 0.7412

P(x>130) = 1 - P(x<130) = 0.2588

(b) What proportion of trees are less than 90 inches tall?

x = 90 inches

z = (90-119)/17

=-1.70588

Probability value from Z-Table:

P(x<90) = 0.044015

(c) What is the probability that a randomly chosen tree is between 95 and 105 inches tall?

For x = 95

z = (95-119)/17

= -1.41176

Probability value from Z-Table:

P(x = 95) = 0.07901

For x = 105

z = (105 -119)/17

=-0.82353

Probability value from Z-Table:

P(x<105) = 0.2051

The probability that a randomly chosen tree is between 95 and 105 inches tall

P(x = 105) - P(x = 95)

0.2051 - 0.07901

= 0.12609

Form a polynomial f(x) with real coefficients having the given degree and zeros.Degree 4; zeros: 1, multiplicity 2; 2i

Answers

Answer:

3

Step-by-step explanation:no