![/ da !! x 1 80, Any = *(4-1)+bm{+-1 +9(+-1) + 9 lt-ig? = (x²21) 4 in (421) + 9133_1] +1 (121 put a = t3 da = 3+2 dt t 3+2 dt](http://img.homeworklib.com/questions/f5b0dc00-12d6-11eb-92a7-f972c96fcf28.png?x-oss-process=image/resize,w_560)
Find dy/dx by implicit differentiation. 19) x1/3y 1/3 = 1
1 (a) Evaluate the integral sz? dx. (32-7) 5 2 7 (b)if s f(x)dx = 3 and 5 f(x)dt = 4, find S f(x)dr. 5
Question 2 please
1 and 2, determine whether or not the integral is In exercises improper. If it is improper, explain why 12. (a) 12 x-2/5 dx 「x-2/5 dx 「x2/5 dx (b) (c) I. (a) 0 13. (a 40 1 dx 2 x 14. (a In exercises 3-18, determine whether the integral converges or diverges. Find the value of the integral if it converges. 15. (a (b)人1x-4/3 dr 3, (a) l.lyMdx (b) x43 dx 16. (a 4. (a) 45 dx...
Theoretical Part 1. Consider the problem of computing f(x)dx, where f(x) could be any function. Letting X1, X2 IID ~U[0, 2, define three very simple estimators: ff(0)f(2), i2= f(X1)f(X2), fi3 = f(X1/2) + f((X2+2)/2) (a) (5 points) Is ft an unbiased estimator of u? (b) (5 points) Is i2 an unbiased estimator of ? (c) (5 points) Is 3 an unbiased estimator of ? (d) (10 points) Compute the variance of each of the three estimator when f(x) x
Theoretical...
(a) Evaluate the integral ſ V1 + 2x dx. 0 1 (b) If f()dx 5 and ) FCD)dz – 3. find i f(z)dr.
Evaluate a) integral 0 to pi (dx/5-4 cos x) b) integral 0 to infinity (dx/(1+x^2)^3)
a.
b.
Solve the IVP -5 3 [= il (x1+[ 6te *) (O)=(-1) -3 Solve the IVP 79 [] = [-* ?] [?]+[6] [70] = [4] 1 0
2. If • a<b<c • Sºf(x) dx = 5 • Sog(x) = 3 • Sg(x) dx = 7 Then, what is the value of f(x) - g(x)]dx?
dx (x+ 1)(x + 3)(x+ 5)(x + 7) 0
dx (x+ 1)(x + 3)(x+ 5)(x + 7) 0
8. Using Chain Power Rule a) ∫ (3X^2 + 4)^5(6X) dx b) ∫](2X+3)^1/2] 2dx c) ∫X^3](5X^4+11)^9 dx d ∫(5X^2(X^3-4)^1/2 dx e) ∫(2X^2-4X)^2(X-1) dx f) ∫(X^2-1)/(X^3-3X)^3 dx g) ∫(X^3+9)^3(3X^2) dx h) ∫[X^2-4X]/[X^3-6X^2+2]^1/2 dx