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All the integrals below are understood in the sense of the Lebesgue.
(1) Prove the following equality which we used in class without proof. As-sume that f integrable over [3; 3]. Then
(2) Assume that f is integrable over [0; 1]. Show that
is di erentiable a.e on (0; 1).
(3) Assume that f is continuous on [0; 1]. Suppose that
Find the full fourier Series of e^x on (-l,l)in its real and complex forms. (hint:it is convenient to find the complex form first)
Utilizes the definition of the limit to prove the given limit. Solution Let M > 0 be any number and we'll have to choose a δ > 0 so that, 1/ x 2 > M
Solve the subsequent IVP. cos(x) y' + sin(x) y = 2 cos 3 (x) sin(x) - 1 y(p/4) = 3√2, 0 Solution : Rewrite the differential equation to determine the coefficient of t
0+50x1-60-60x0+10=
The longer base of a trapezoid is three times the shorter base. The nonparallel sides are congruent. The nonparallel side is 5 cm more that the shorter base. The perimeter of the t
Solve the Extraneous Solutions ? You're worst enemy (aside from arithmetic mistakes), while you're trying to solve a rational equation, is forgetting to check for extraneous so
INTRODUCTION : The other day I overheard 6-year-old Ahmed explaining to his older sister about why swallowing the seeds of an orange is harmful. He said, "The seed will become a p
jamal works every morning in his garden. yesterday he worked 3 AND 3-4HOURS. HE SPENT 1-3 OF THE TIME PULLING WEEDS. HOW MANY HOURS DID JAMAL SPEND PULLING WEEDS?
What are the characteristics of a queuing system? (i) The input pattern (ii) The queue discipline (iii) The service mechanism
what is a domain of a function?
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