12.)Express lim E(3(x;,)² – 5x, + 2)Ax as a definite integral on the interval [0,1]. i=1

Q: Determine if the function f(x)= is continuous -- sin(x) x on the interval I= (0,1).

A:

Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

A:

Q: Find ♬ as a function of x and evaluate it at x = 0, x = π/6, and x = π/2. -["sin e de Ꮎ F(x) F(0)…

A:

Q: points

A:

Q: (x. v) = (0, 0)

A:

Q: sketch f(x)=sec x over the half-open interval -r,27). 2 1 3/% 27t 52

A: Given query is to find sketch the graph of sec(x) .

Q: 2.6. Let ƒ be continuous on [0, a]. If x e [0, a], define fo(x) = f(x) and let %3D 1 fa+1(x) = -…

A: We will use the basic knowledge of integral calculus to answer this question. Note that we can only…

Q: f(0) = sec0 is one-to-one on the interval [O,π] with π/2 removed.

A:

Q: 77. Show that if f is a quadratic polynomial, then the SDQ at x = a (for any h + 0) is equal to…

A:

Q: 4. Find the absolute extrema of f(r) = 7r/3 - r7/3 over the interval [-8, 8].

A: Given function is

Q: A1). Sketch the graph of ONE function such that ALL of the following hold: i). f"(x) 0 for x> 2…

A: Graph of function

Q: Sketch a graph of a function f with the following properties. f' 0, for -70 and f''>0, for -50 and…

A: f'<0 and f''<0 for x<-7 f'<0 and f''>0 for -7<x<-5 f'>0 and f''>0 for…

Q: fn. (1,00) Evaluate lim

A:

Q: 5. If f(x)=3*-9 and g(x)= tanx, then what is the domain of (g+f)(x) on the interval [0,2m]?

A: For the given question, we can write the function (f÷g)(x) as:f(x)g(x)=tanx3x-32Hence, the domain of…

Q: 1. Function f is continuous on (-00,00). Find constant k. f(x) [kx² + 2x x-kx if x ≥ 2 if x < 2

A:

Q: Write the composite function in the form f(g(x)). [Identify the inner function u=g(x) and the outer…

A: The given functions, 1. y=tanx6 2. y=x5+9 3. y=e7x We have to write the functions in composite form…

Q: 3. Verify that the function f(x) defined over the interval [0, 3], satisfies Rolle's theorem. Find…

A:

Q: Assume that h[n]=(-1)"g[n]. What is the relation between H(2) and G(z) o HZ) = (- 1)" G(z) H(2)…

A:

Q: lim , E C [2,4| 1/2

A: The solution are next step

Q: 1. (Bx2 |x- 61-8 for x> 2 (a) For what value of Bis the function f(x) = }", for x 2 continuous atx=…

A:

Q: 3. Determine whether f is differentiable or not differentiable at 1. (x – 1 if x > 1 (-x² _if x <1…

A: If a function is differentiable at any point x=a ,then its L.H.D. =R.H.D.

Q: . There is a function f that's continuous at 0 and f(x) = f(2x) for all x's please show that f must…

A: Answer for sub question 1a: First step is to show fx=f2-nx for each integer n≥0. If n=0: fx=f2-0x…

Q: 2. Determine whether the Mean Value Theorem applies for the function over the given interval.…

A: We Know that the Mean Value Theorem states that if f is continuous over the closed interval [a,b]…

Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.