f'Lx) = 2x (x+4) a) whent cre the Critical points? do es it increase and de crease ? -on unien intervals were

Q: Suppose that Xis a continuous unknown with 5< X< 5 and having PDF denoted fsatisfying f ( x ) = c (…

A: Given: fx=c×25-x2                  -5&lt;x&lt;5

Q: Approximate the region under the curve f(x) = x^2 by using the Riemann sum with 3 intervals using…

A: Given, upper limit= b=14 lower limit = a= 2 number of intervals= n=3 We first have to find the width…

Q: Approximate the region under the curve f(x) = 2x + 1 by using the Riemann sum with 3 intervals using…

A: Width of each interval= (21-3)/3=18/3=6 so the partition is 3,9,15,21 For left Riemann sum we take…

Q: f(x) = log5 (2x + 1).

A: To  Determine:  Interval of convergence  f ( x ) = log5 ( 2x +1)

Q: Find the rate of convergence for lim h-0 sin h - h cos h2 0.

A: Given that limh→0sinh3-h3cosh2h=0. The rate of convergence can be calculated by evaluating the…

Q: Find the radius of convergence for Σ (sin²n)x". n=1

A:

Q: The error is numerically computing the integral | 1 dx using the +4 trapezoidal rule with two…

A:

Q: How are the derivative and the integral of a series of powers defined?

A: Consider the following power series with a radius of convergence R &gt; 0. Let

Q: 12)Use the Trapezoidal Rule to estimate the integral ₁√x² - 1 dx using 4 intervals. Round to the…

A: Solve the following

Q: How does the interval of convergence (the derivative and the integral) behave.

A: The interval of convergence of the derivative and the integral is discussed here.

Q: nich integral represents the length of the graph of y = In(1 – x²) over the interval [0, ]:

A: here option A is true because length is given by =1+(dydx)2dx so here…

Q: 10. Determine whether | sin(x)dr converges or diverges. If this improper integral converges,…

A:

Q: integrate f(x) =x^3 * exp(1.33*x) from 1.26 to 2.01 with simpsons 3/8 method use 21 intervals for…

A: Given that, f(x)=x3(e1.33x) , from 1.26 to 2.01 with 21 intervals  To determine The integration…

Q: Find the critical value z/2 that corresponds to a = 0.09. %3D Za/2 = (Round to two decimal places as…

A: Solution: From the given information, α=0.09.

Q: Determine whether it converges or diverges. You must provide justification for your answer. sin(x)…

A:

Q: –1 dx x V In (-x) -3

A: Find the type of the generalized integral and examine its convergence.…

Q: The values of a that make the integral Tdx converges

A:

Q: dx 3) L. Vx+1

A: Given:

Q: Q2. Give a counterexample about a bounded function that is not Riemann integrable.

A:

Q: 8 Use right endpoints and 3 intervals to estimate S dx. 2

A:

Q: •4 x dx 10 x2 – 9

A:

Q: What are the critical points of sin(x2-1), at the closed interval [-1,1]?

A: Given: The critical point is a funtion is the point where the derivative of the funtion is zero.…

Q: Find the number of subintervals that will ensure that the absolute error in approximating the…

A: Using Simpson 1/3 rule.

Q: Determine whether dx is convergent or divergent. If it is convergent evaluate the integral Vx 3. 4…

A:

Q: 6 Jlgul sin (nx +3) 1,(x) =- is convergent point wise to zero function. n-1 ylgn O Ihi O

A: Calculate limn→∞fn:  limn→∞fn=limn→∞sinnx+3n-1             =0

Q: If X; derive the moment-generating function (mgf) of X?. Ν (μ, σ) :

A: Given X~ N(mu, sigma^2) We want to find the mgf of X^2

Q: If the Midpoint Rule is used on the interval [-1, 11] with n = 3 subintervals, at what x-coordinates…

A: Consider the interval a,b=-1,11n=3. The length of interval, ∆x=11+13=4 Class intervals…

Q: Determine whether integral 0 to pie /2 sec x dx    converges or diverges

A:

Q: х — 3 х3 -4х

A:

Q: plot Y funetion of as over Hhe Peenge ☺.0l <*< l00.

A:

Q: The integrals converge. Evaluate the integrals without using tables

A: Evaluate the integral ∫0∞16tan-1x1+x2dx.

Q: (a) Use the Midpoint Rule with n = 10 to approximate the integral. (b) Give an upper bound for the…

A: To evaluate the definite integral by the midpoint rule and the error bound, use the  following…

Q: -x² xe* dx -00

A: Given: ∫-∞∞xe-x2dx

Q: of P converges Find the Value which the integral absoluley condition. Sin () dx

A: To find the value of p for which the integral ∫1∞sin(1x)xpdx  converges absolutely. The improper…

Q: rmine whether sin z is convergent.

A:

Q: Show that integral - infinity  to infinity  x dx is convergent or not

A:

Q: Which of f (x) = x sin2 x and g(x) = x2 sin2 x has a larger average value over [0, 1]? Over [1, 2]?

A:

Q: If the Midpoint Rule is used on the interval [- 3,27] with n = 3 subintervals, at what x-coordinates…

A: given  Interval [-3,27] and n = 3,  the number of sub intervals. To find at what x-coordinate at…

Q: Examine the convergence of the integral.

A:

Q: In n n=2

A: The given expression is, ∑n=2∞lnnn The integral test says that for a series ∑n=2∞lnnn converges if,…

Q: cises 1–12 con- of the Integral

A:

Q: 55. Show that dx J+4 converges by comparing with x³ + xdx. -3 dx. х

A:

Q: - Show that sin converges. Hint: Use sinx <x for x 2 0.

A: Given: The series ∑n=1∞sin1n2, To show:  The given series is convergent.

Q: Use the composite Simpson's rule with step length h=0.5 to determine 1= [ (2x - - 3x2 + 4x – 1)dx,

A:

Q: Sind the Partial derivadiVes of th Jiven fuctions with Ves Pect x(2-CoS 2y)

A: We have to find the partial derivatives.

Q: Find the critical value zα/2 for α=0.05 Round to 2 decimal places.

A: Given data: α=0.05 Find the critical value zα/2 ( Round to 2 decimal places)

Q: 1+sinx dr dx 8. Use the Comparison Test to test for convergence.

A:

Q: is Hhe followin integen I wbich Va lu es convergent? dx

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.