basic calculus problems.

24) Let f be a differentibale function defined on the closed interval [a,b] and let c be a point in the open interval (a,b) such that. I f'(c)=0 II f'(x)>0 when a ...continues

Basic claculus problems.

36)If the functions f and g are defines for all real numbers and f is an antiderivative of g, which statements are not true? I If g(x)>0 for all x, then f is increasing. II If g(z)=0 then f(x) has a horizonatl tangent at x+a. III If f(x)=0 for all x, then g(x)=0 for all x. IV If g(x)=0 for all x, then f(x)=0 for all x. ...continues

basic calc problems

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 Reiman 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 ...continues

Riemann Sum

Write out the Riemann Sum R(f,P, 1, 4), where f(x) = ln x, P = {1, 2, 2.4, 2.9, 3.4, 4} and ck is the midpoint of the interval [xk−1, xk] for each k. Get a decimal approximation for the Riemann Sum.

Area of an Region

Find the area of the region {(x, y)|0 <_ y <_ x3 − 12x + 6, 4 <_ x <_ 6} <_ is to be taken as less then or equal to

Find the area of an region

Find the area of the region bounded by the graphs of y = x2+3x−1 and 25x−3y = 19.

Riemann Sum

Write out the Riemann Sum for R(f,P, 0, 2) for arbitrary n, f(x) = x2−3x+2, where each ∆xk = 2/n and ck = xk, simplify and use the formulas ∑n,k=1 k=(n(n+1))/2 and ∑n,k=1 k2=n((n + 1)(2n + 1))/6 to find the limit as n --> 1.

Simplify

Simplify: ∑n,k=1 (k + 5)*(k − 1)

Sum & Calc

Write out the sum ∑7,k=3 (k2 − 3k + 1) and calculate it.

setting up a riemann sum

I can't figure out exactly how to formulate a riemann sum. For example, when given y=x+2; [0,1], and told to "find the area of the region under the curve y=f(x) over the interval [a,b]. To do this, divide [a,b] into n equal subintervals, caluculate the area of the cooresponding circumscribed polygon, and then let n go to infin ...continues