34) The function f is continuous on the closed interval [1,5] and has values that are given in the table below. If 2 subintervals of equal length are used, what is the midpoint Reimann sum approximation of integral with 5 on top and 1 on bottom f(x)dx?
Please given step by step explaination and answer is 32.

x 1 2 3 4 5
F(x)15 10 9 6 5

33) Let f be the function defiend by:
F(x) = x^2-25/5-5 for x does not equal 5
F(x) = 0 for x=5
Which statement of f is true?
I. lim as x approaches 5 of f(x) exists.
II F(5) exists
III F(x) is continuous at x=5.

Please also tell why also false?

Solution Summary

A reimann sum is investigated and the existence of a function is discussed. The solution is well presented.

1. Write a Reimannsumand then a definite integral representing the volume of the region, uisng the slice show. Evaluate the integral exactly. ...
2. Find the volume of a sphere of radius r by slicing. ...
[See attachment for questions.]

Consider The Following Function:
(See Attached File)
Calculate the Upper and Lower Reimannsums based on an arbitrary partition
P = {xo, .............., xn} of [a,b] and then compute the upper and lower Reimann Integrals of D (5x-11) over [a,b]. Prove that f is not a Reimann Integral.

If f is a reimann integrable function on [a,b], and if [c,d] is a subset of [a,b], prove that f is reimann integrable on [c,d]
hint: if P is any partition of [c,d], P can be extended to a partition P* of [a,b] with ||P*|| <= ||P||. Show that
U(f,P) - L(f,P) <= U(f,P*) - L(f,P*)

Are these functions Reimann Integrable? I am just learning this topic, so my description may not be accurate. A function is Reimann Integrable if it's Upper Darboux Sums and Lower Darboux suns are equal.
Or stated another way, if U(f, P) - L(f, P) < e
The two functions are piecewise functions.
1) f(x) = { 0 when x =

Taking the continuity of h(x) as given in#30026,#30028
by using any of the functional limitsandcontinuity theorems prove that the finite sum g_m (x)=sum sign(oo top n=0 bottom) of 1/2^n h(2^n x) is continous on R

1. Solve log₆x-3=0
2. A business owner is comparing the costs of purchasing inventory and the profit from the sale of the product. The relationship proves to be linear. Which type of variation will describe the data?
Direct as nth power joint regress
Inverse direct
3. Solve x²-25<0
4. What is the

Please refer to the attached file for the proper formatting.
Suppose I C R and J C R are intervals, f : I --> J is uniformly continuous, and g : J --> R is uniformly continuous.
a) Give the definition of h=g dot f. What is its domain?
b) Prove that h is uniformly continuous.

** Please see the attached PDF for the complete problem description **
Show all work and a step-by-step solution so that I can clearly see how you arrived at your answer.
No calculators or computer programs can be used to solve this problem.
Thanks