The following table shows the annual number of PhD graduates in a country in various fields. 1990 1995 2000 2005 2010 Natural Sciences 70 130 330 490 590 Engineering 10 40 130 370 550 Social Sciences 60 110 270 470 830 Education 30 40 130 210 520

Q: 50 (e*-2)(e2x + 1) et dx

A:

Q: y aln(a) – y = 0; y(2) = In(4)

A:

Q: sech Vt tanh V dt Vi

A: Given : Intergral sech √t tanh √t dt / √t

Q: 32 8y%dy y-15 2.

A: The given integral is,

Q: 1 Evaluate dx. 4+e-3а 1 dx 4 + e-3x + C %3D

A:

Q: (3) Let X = n(µ,4) and Var(2x) = E(4-7x) find u.

A: Given,X~n(μ , 4)

Q: Find a power series for each of the following, centered at a = 0 for parts (a) - (d) and centered at…

A: The function f(x)  is a rule that associates or fixes a number to the particular point x. Derivative…

Q: Jp-1(x) – Jp+1(x) = 2J,(x), %3D

A:

Q: how did you get the z a/2?

A: how did you get the z a/2?

Q: P(A | B) = 0.1, P(B) = 0.7, P(A | B') = 0.4. Find P(B | A).

A:

Q: V- 2 dx +1)

A:

Q: Show that esin(x²)dx < e– 1.

A:

Q: p(x) = x / 5 x = 1,0,1

A: Given, p(x) = x / 5 ;        x = 1,0,1

Q: IPydx dy 20.

A: To evaluate: ∫02∫13 x3y dxdy

Q: x(x2 + 1)3 dx J-1

A: Consider the integrals, ∫-11xx2+13dx…

Q: 1- fº, SÉ, x² e*Ydxdy 2

A:

Q: Evaluate e dt 0.2

A: We have to use standard gamma integration here.

Q: Find P(A and B')

A: P(A) = P(B) = 0.33 P(A or B) = 0.43

Q: d³x d2x dx -2- =0 dt dr3 dr?

A:

Q: Solve for L fo=

A:

Q: (a) / | Va? (а) /a² + x² dx

A:

Q: Let f(x, y) = (- (3x + y))'. Then %3D drðy af

A:

Q: 2Linear edluotion 5. dy dx

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…