Determine if the following statement is true or false. b If f is continuous on the interval [a, b), then f(x) dx is a number. a Choose the correct answer below. O A. The statement is false. It is only valid if f is a positive function, in which O B. The statement is true. If a function is continuous on a closed interval, t must be a real number. OC. The statement is true because the integral of any function must be a re -D. The statement is false because the value of the integral might be oo. E. The statement is false because the integral might be undefined.

Q: decide if the given statement is true or false,and give a brief justification for your answer.If…

A: The given function gt=1sin t,if t is not a multiple of π0,if t is a multiple of π is piecewise…

Q: 3. Let f be a function from X into Y. Suppose A and B are subsets of X. Prove that f(A U B) = f(A) U…

A:

Q: Suppose and z are functions of x and y, then prove.

A:

Q: Determine whether each of these functions is injection, surjection or bijection from R to R.show the…

A:

Q: Find the value of a such that f is continuous on the entire real line. Write the exact answer. Do…

A:

Q: Let f:2+ +2 be the function defined by if n>l00 f(f (nt 11)) othe rwise fln) ={ n-10 what is the…

A: Function does not terminate. So values is -1.

Q: if r 4,

A: Given function is, gx=x           if x≤03           if 0<x≤13-x2   if 1<x≤4x-3     if  x>4

Q: f(x) x-1 x + 10x 11 x = -11 and x = 1 -

A: For continuous so the denominator of the function not equal to zero

Q: t "a and "b" such Find the constant that the function is continuous on the entire real time. 7,…

A:

Q: For each of the questions below, indicate if the statement is true (T) or false (F). (a) Any…

A: answer  is next step . as per guideline i can only answer 3 question .

Q: Use the definition to prove that the function in f(x) = 2x-3 is uniformly continous.

A:

Q: Eind the value of the constant c that makes the following function continuous on (-o, ∞). if y €…

A: By using conditions of continuous function.

Q: Show that the function is continuous only at x = 0. (Assume that k is any nonzero real number.)

A: The given function is fx=0    if x is rationalkx   if x is irrational where k is nonzero. Note that…

Q: Let f be a measurable function ,then |f| is measurable .

A: Statement is correct see the step 2

Q: D. For what values of a and b is Continuous at every x? -2, - b, f(x) = 3, -1 <x < 1 ах

A:

Q: ㅏ 5π 12 y = - 2x + sin 4x, 5п 12 SXS 5п 12 X 5T 12

A: The equation of function is y=-2x+sin4x

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.