Evaluate the following integrals (from A to E) A. Integration by parts i) ſ (3+ ++2) sin(2t) dt ii) Z dz un (ricos x?cos 4x dx wja iv) (2 + 5x)eš dr. B. Involving Trigonometric functions 271 п i) | sin? ({x)cos*(xx) dx ii) Sco -> (=w) sins (įw) iii) sec iv) ſ tan” (63)sec^® (6x) dx . sec" (3y)tan?(3y)dy C. Involving Partial fractions 4 z? + 2z + 3 1) $77 dx 10 S2-6922+4) dz x2 + 5x -...
SIDE A Part I. TRUE OR FALSE QUESTIONS. 1. S* x sin(x) dx = x = x So* sin(x) dx. A. False B. True 2. / ze*dx + ***dz - / redz A. True B. False 3. 5* 5 sin(x) dx = 5 * sin(x) dx. A. True B. False 4. ds "ninta) dir = * = sin(a) dår. A. False B. True 1 5. یة x2 dx = 0 3 B. False A. True A. False B. True *...
I'm stuck on this question, please help! Question 1. Consider the following claims: (1) So g(x) f(x)dx = SØg(x)dx · SOF(x)dx holds for all f and g continuous. (2) If f(x) is such that So f(x)dx = 0 then f(x) = 0 for all 0 < x < 1. (4) If f is continuous in [0, 1], then is bounded, independently of the value of n. The sum of all correct statements equals:
Write DNE if the limit does not exist at a point. 1. lim g(x) = -1 Help on limits. 2. lim g(x) = 3 3. limg(x) = 0 M 4. lim g(x) = -4 5. g(1) = 2
Question 1 12 Evaluate: So x2 arctan(x) dx = HTML Editor B I y A - A - IX EE 3 7 2 xx, 5 E * CV TT: 12pt
If ∫43f(x)dx=−5 and ∫−1−2g(x)dx=3, what is the value of ∫∫Df(x)g(y)dA where D is the rectangle: 3≤x≤4, −2≤y≤−1?
1.Z=f(x,y)=6x+7y where i) x=g(x)=x^2 y=h(x)=x^4 and ii )x=g(x)=x and y=h(x)=x^3. Please calculate Total derivative by applying this formula dZ=Zx dx/dx +Zy dy/dx
(b) I G)(u) and G'(1) = 2+e Ft2): 3gcx1+1α)-x'(x) faf(x) , compute G(1) and G'(1). g(5a)' 2x for 37 Problem 2 For each function below, find the smallest integer n for which f)0 and find fin-(x) or explain why this is not possible. notation: The factorial function is n!n (n -1).(n-2)3.2.1 example: If (x)2+z2-1, then n 5 andf)24.3-2.1 2(41). (a) (x)95 16z +23. (b) f(x) sin(3z). Problem 3 3 is shown to The graph of the tilted ellipse z2 -...
Need help with MATLAB, what code should be added to print the graph of the trapezoid rule code below? %%Matlab code for Question 5. syms X y intlx exp(x),0,2); %integration of x*exp(x) fprintf("htlntegration of x"2*exp(x) for [O 3] is %2.5f.\n,y) %Integration using Trapizoidal rule nn [100 1000]; for ii 1:2 a:0; b-3; %Integration limit ns-1:nn(i) integral Values-zeros(size(ns)); ourFunction-@(x) x.*2.*exp(x); for n-ns val(n)-trapizoidal (ourFunction,a,b,nn(i); end fprintf nlntegration of x 2*exp(x) using Trapizoidal rule for [O 3]\n') fprintf('1tTrapizoidal integration value for n-%d...
3. Evaluate using the correct form -dx 0 x-2 4. Consider the sequence 3n n+1 Does the sequence converge or diverge. If it convergés, to what does it converge?