Let fand g be continuous on the closed interval [0,5]. Suppose that / f (x) dr =A, / f(x)dx=B, 8(: dr=C_ The definite integral S'v)-s(x)]d« is equal to A А -В+С B В - А —С В -А+С D А -В —С
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- consider the functions g(x)=x^4 and k(x)=x^5. if x^5-x^4 is equal to 0 ->x=0 or x=1, represent the area enclosed between g and k on the interval [-1,2] in terms of definite integrals without using absulte value signs.Suppose f (x) is a continuous real-valued function. Show that \int_{0}^{1} f (x)dx = 1/3 f (c) for some c in [0, 1]Suppose that f is an integrable function on R (real numbers). How do you show that the integral of f(x) exp(x2/k) converges to the integral of f(x) as k goes to infinity? Here exp() denotes the exponential function with base e.
- Let Q = Q(K, L, t), where K is capital, L is labor, and t is time. Both capital and labor as also functions of time, such that K=K(t) and L=L(t). Use total differentiation to find and expression for the total derivative dQ/dtShow that f is continuous on (-infinity, +infinity) f(x)= { 1- x2 , if x less than or equal to 1 { ln(x), for x > 1Evaluate the f.f integrals
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