∫_0 ^1 ((Li_3 (−x^2 ))/(1+x))dx
if f(2) = 3 and f(4) = 5 find ∫_2 ^( 4) f(x) ∙ f^′ (x) dx = ?
Let f(x) and g(x) be given by f(x)= (1/x) +(1/(x−2)) +(1/(x−4)) + ... +(1/(x−2018)) and g(x)=(1/(x−1)) +(1/(x−3)) +(1/(x−5)) +...+ (1/(x−2017)). Prove that ∣ f(x)−g(x)∣ >2 for any non−integer real number x satisfying 0<x<2018.
There is a field. Everyday kids throw some balls on the field. At night the farmer goes and place the bucket in a place where it will contain the most amount of balls. the field can be represented as a line of length 10. the bucket can be represented as a line of length 2. If the kids have thrown 3 balls into the field, what is the probability that the bucket will contain 2 balls how a sample looks like Where the blue line represents the field. and the red line represents the bucket. and the dots are the balls
A truck, P, travelling at 54km/h passes a point at 10:30 am while another truck, Q travelling at 90km/h passes through this same point 30 minutes later. At what time will truck Q overtake P?
Find: (2/(35)) + (2/(63)) + (2/(99)) + (2/(143)) = ?
{ ((sin(x+y)=cos(x−y))),((tanx−tany=1)) :} (x,y)=(?,?)
cosx−(√3)sinx=1 x=?
prove that ((1−cosA+cosB−cos(A+B))/(1+cosA−cosB−cos(A+B)))=tan(A/2)∙cot(B/2)
2025^(2025) = x (mod 17 )
by diffention find f ′(z) of f(z) = (z)^(1/3)