15.B. Show that a polynomial function f, given by f(x) anx" + an-1x"¬1 +... + a1x + ao, x€ R, is continuous at every point of R.

Q: 2. Determine with justification, the absolute maximum and minimum of the function below in the…

A: We have to find the absolute maximum and minimum of the function in the associated interval.

Q: Prove algebraic ally that any function of the form f(x)=ax2n+4 (where n is an integer) is symmetric…

A: The given function is fx=ax2x+4. To prove fx=ax2x+4 is symmetric to the y-axis, it is enough to…

Q: 13. When is a polynomial f(x) of at most the order of a polynomial g(x) as x→∞? Give reasons for…

A:

Q: Find the constant a such that the function is continuous on the entire real line. 7sin x if x < 0…

A: Here we find the value of constant a

Q: Suppose f is a function which satisfies the properties: f(x + y) = f(x) + f(y) + x²y + xy? for all…

A: Given that, f(x+y)=f(x)+f(y)+x2y+xy2 for all real numbers 'x' and 'y'  and, limx→0f(x)x=1   As we…

Q: 10. Determine whether the intermediate value theorem guarantees that the function has a zero on the…

A:

Q: For the function x2 +3 for x 2 | Identify the discontinuities of f as removable, jump, or in…

A: Given information: The function is hx=x2+3    for  x&lt;110-x   for  1≤x≤26x-x2  for   x&gt;2.…

Q: (a)Verify Rolle's Theorem for f (x)=x - 16x+10 over the interval [0,4].

A:

Q: 02: Let f(x)= x' – 7x+ 2, 0sxs1. 1. Show that f(x) has exactly one real root in the indicated…

A: Answer

Q: 1. For what value of k is the function h(x) continuous on the whole real line? HINT: Use definition…

A:

Q: 15.C. Show that a rational function (that is, the quotient of two polynomials) is continuous at…

A: I have proved that if g(x) is continuous at a then 1/g(x) is continuous at x=a provides g(a) not…

Q: 5. Prove that the function f: Z → Z defined by f(x) = 3x + 1 is one-to-one.

A:

Q: 2. Determine whether the function y= -x5 + x3 – 1 is even, odd, or neither. Justify your ans wer.

A:

Q: 2. Let R be a U.F.D. and f (x), g (x) e R [x]. If f(x) g (x) is a primitive polynomial, then f (x)…

A:

Q: Which is the correct conclusion about the function h(x) ={V4- x2 if x - 3 if h has a removable…

A: Given function is: hx=-x-2    ;  if x&lt;-24-x2     ;  if -2≤x&lt;2x-3  ;  if x&gt;2 We have to…

Q: Q2:Check the continuityof the functionf(x) at x-0,1,2,3, and 4, Where:(25 degrees) 2- x 2 f(x) = | 3…

A:

Q: If f(x) = x² -2x, which of the following represents f'(1)? (I+h)'-2(1+ h)-1 lim h² +1-2(1+h)+1 lim…

A:

Q: c. Consider the compound function: 2|x| for h(x) V(5 +x) - V5 for 0<x<5 %3D (Vx -5)2-25 (x2 - 25)…

A: Given,  h(x)=2|x|                             for  x≤05+x-5(x-5)2-25         for     0 &lt;x…

Q: . Show that the function f: R→ R defined as f(x) = 13x − 15 is one-to-one.

A:

Q: Consider the graph of the function f(x) = 3- 2x - x2: 5 -1 -1 -3 -5 -4 -3 -2 -5 -7 -9 -11 The area…

A: Given the graph of fx=3-2x-x2

Q: Determine the c which satisfy the conclusion of Rolle’s Theorem for the given function and interval.…

A:

Q: Determine b so that f(x) is continuous if O 8 x + 6 xS 6 f( x ) = D O 2 x2 + bx +10 x > 6 b =

A:

Q: 19. Suppose f is a piecewise-defined function, equal to g(x) if x 2, where g and h are contin- uous…

A: Consider the given piecewise function. f=gx      x&lt;2hx      x≥2 The functions g(x) and h(x) are…

Q: Consider the following statements 1- The function f defined by f(x) = x³ is decreasing in R 2- If a…

A:

Q: Let f(x) = x -[r] and f :[1,5) →[0,1). What is the discontinuously type of f(x) at the point x = 3?

A:

Q: Q3) Test the continuity of the function f(x): -15x <0 0S X< 2 F(x) = 2х— 1 x+ 3 X = 2

A:

Q: 3. Determine the value of c such that the function is continuous on the entire real line. x+3, x 2

A:

Q: Let f(x) = -. Does f(-2+h) equal or -2 +h :-2 with h = 0.5. Compute the difference quotient at a = +

A: Given: fx=1x

Q: , for x 1 Let f(x) be a function de fined by f(x)3= Discuss the contuniuty of f andf".

A:

Q: 3. Use the Intermediate Value Theorem to show that f(a) = a2-3x +1 has at least one real zero…

A: According to intermediate value theorem, if f(x) is a continuous function whose domains contains the…

Q: Find the continuity of the function Of(x)= tx²+3 と+ とく3 5x-3 at =t

A:

Q: Assume that f(x) is a function defined by x²-3x+1 f(x) = 2x - 1 for 2 ≤ x ≤ 3. Prove that f(x) is…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Define g(-1) in a way that extends g(x) = 1 to be continuous at x= - 1. x² -x-2 2 9(-1)-D

A: Given that: g(x)=x2-1x2-x-2

Q: let f: R^ -> R be a function given by 2 f(x₁, x₂... x₁) x.x²2. x²n, where = € 2.1 Show that the…

A:

Q: 12. When is a polynomial f(x) of smaller order than a polynomial g(x) as x→00? Give reasons for your…

A:

Q: Apply Corollary 2 to the Intermediate Value Theorem. f is a polynomial and continuous everywhere.…

A: Given that, f(-3) = 170 &gt; 0 f(-2) = -25 &lt; 0 f(-1) = 2 &gt; 0 f(0) = -1 &lt; 0 f(l) = 2 &gt; 0…

Q: Find x for which f(x) is not continuous: 3 x-1 f(x) =-+ x'x2 -1

A:

Q: 3. Determine the value of a so that f(x) is continuous on the entire real number line when: f(x) =…

A:

Q: Show that the function f : R → R given by f(x) = x3 is injective.

A: To show the given function is injective(one-one), first calculate the value of function at two…

Q: O Show that the function f: N2 N defined by f(x, y) = 2X3Y is injective but not surjective.

A:

Q: 1-→Proof-that-this-function-is analytic Fla)=z1

A:

Q: 3. Give an example of a function f.N→N which is surjective but not injective.

A:

Q: Give an example of a function f : R → R that is continuous at x if x is an irrational number, but it…

A:

Q: (-x3 – 4x + 20 ,x > 3 2 – 7x , x < 3 Determine whether the function f(x) = is continuous at x = 3.…

A: From the given problem: fx=-x3-4x+20 , x&gt;32-7x , x≤3 As we know that:  If limx→a+fx=limx→a-fx=fa…

Q: Let g(x) = x2 – 4/x2 – 3x -10 Determine x-value(s) for which g is not continuous

A:

Q: D. Discuss the continuity of the function on the closed interval. Function Interval 1. g(x) V49 [-7,…

A: Note: We are entitled to solve only one question at a time. Given: gx=49-x2 To Discuss: Continuity…

Q: Consider the function f defined by the formula ( ax2 + bx – 3b if x 1. Determine the values of a…

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.