k is the last two digit of your student ID (For example; if student ID=110060109 k-09) Question Evaluate the following integral: (1- exp(-k* *))dr by; (a) analytically, (b) single application of the trapezoidal rule (sampling time(dx)=4), (c) composite trapezoidal rule (sampling time(dx)=2), (d) single application of Simpson's 1/3 rule (sampling time(dx)=4), e) composite Simpson's 1/3 rule with (samnli f) single annli

Q: x²–1 For S dx,x

A: Given,             ∫x2-1xdx

Q: sinh x 1+ cosh x

A: sinh x1+cosh x

Q: 1/2x (In2) In x (use L'hopital's Rule)

A:

Q: There is an average of four accidents per month at an intersection. Assume that a month has 30 days.…

A: The variable X is defined as the number of accidents. There is an average of four accidents per…

Q: f(x)=square root of x from a=3 to b =6 area under curve

A:

Q: L, x*e*** dx 3+1

A: 3.1) ∫-12x2e(x3+1)dx Let u=x3+1 du=3x2dx

Q: Evaluate 1 e* +e*

A:

Q: S cor* (***) csc (*) da 3x+1) 3 3x+1

A: Solution…

Q: 2. Se* sin(e) dx

A:

Q: where did 0.025 come from? please explain the steps to get critical value

A: The level of significance is 0.05.

Q: L{sinh 6t– cosh t

A: we have to find the value of L{sinh(6t)-cosh(t)}

Q: 2) dx -

A: We will solve the integration by the substitution, t = ex

Q: Consider the intergral of (2x + 1) dx from 1 to 5 Estimate its value using 4 and 8 subdivisions of…

A: Note:- In given problem, you don't mention Simpson Rule name (Simpson 1/3 Rule or 3/8 Rule). Due to…

Q: Find the total diffedrential  w = x^16yz^4+sin(yz)

A: w = x16yz4 + sin(yz) Total differential  dw =wxdx + wydy +wzdz

Q: (i) x' ^y

A: Solution 1: Conjunctive normal form⇒ meet the maxterm   Given x'∧y                    (1) We know…

Q: d dx (f³x²) = ○ 6x63x² (In b) ○ 6³x² (6 ln b) 6x6³x² ○ xb³x² (ln(6b))

A:

Q: In(cosh x + sinh x) + In(cosh x – sinh x) = - 1 -1 Leave Question 2.

A:

Q: -Tt /12 SK1 tan* (3x) dx

A: We have to compute the integral  . First, consider the integral . We can write it as:

Q: Area under the curve y2 = 4x from x=1 to x=4

A:

Q: "INT" function (alternative name is "Floor" function) returns integer value closest to the Input…

A:

Q: In Problem 5, you found the closed formula for the sequence below. Use proof by induction to verify…

A:

Q: Show /x^ In х dx xn+1 ((п + 1)In x — 1) (п+1)2

A:

Q: find integal x over square root 4+x dx by any method.

A:

Q: Prove inf { ☆InEN}=0 sup { inen}= Prove sup?.

A: We have to prove that Inf { 1/n | n in N } = 0 Consider the set of all lower bounds, then 0 lies in…

Q: Ssin(Tx)cos (3Tx)dx

A: We will use the formula Sin (A) Cos (B) =1/2[Sin (A+B) +Sin(A-B)]

Q: the function f(x)=1/2x^2+1 find the area under the curve of f(x) from 1 to 4 using upper and lower…

A: Given the function is: f(x)=1/2x2 +1 We need to find the area under the curve of f(x) from 1 to 4…

Q: Q5// Evaluate *x5*(1+ln x)dx.

A:

Q: 9> 2.3* (sin (20x) +e^l.53x) > 0 find x

A: Given: 9≥2.3*(sin(20x)+e1.53x)≥0

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.