Please help with the following questions!

Evaluate the definite integral. The error function, used in probability, statistics, and partial differential equations describing diffusion, is defined as: 16 6 2 X erf(x) = dx erdt. X 7 Find erf(0): Answer: erf(0) = 8 Given that 13 f( x)dx = 14 and / f(x)dx = -1 Evaluate the following limit: find: 5 lim 5kin 9 5 's s ( )dx = 10 n K=1 The Fresnel function S(x), used in optics, is defined as: Consider the function F(x) - be " dt. Find F' (x): S( x) = / sin (12 ) dt. 12 F' ( x) = Let F(x) := S(x3 ). Find F' (x): F'(x) =