(a) f :Z → Z, where f(x) = x². g : Z → Z, where g(x) = |æ|². %3D (b) f :Z × Z → Z, where f(x, y) = |r + y\. g : Z × Z → Z, where g(x, y) = |æ|+ \y|-

Q: 1. Show (in terms of e- 6) that a function f : R* → R defined by f(x, y, 2) = (2x + 3y + 42) is…

A:

Q: Whch of the futowing tunction is a iner tunctiont Sx)- V3x -4 S(x) = x +5 O oton O outen f(x) = 2x…

A:

Q: Discuss limit(n →∞)fn on B and C for  fn(x)=x/n; B=E1; C = [a, b] ⊂ E1 fn(x)=(cos x + nx)/n; B=E1

A: Note: Since you have not mention anything about the set E1, We are considering it any sunset of real…

Q: 22 dt at x = 4. ind the linearization of f(x) = 7 - 4 +t

A: Consider the given function fx=7-∫7x+3224+tdt

Q: b) Show that the “energy function" E(x, y) = 5 + is non-increasing along the solution, i.e., using…

A: (b) The objective is to show that the energy function  is non increasing along the solution, that…

Q: 1.lf f(x) and g(x) are continuous functions, then SIF(x) ·g(x)] dæ S f(x) dæ · ƒ g(x) dæ. 2.lf G(x)…

A:

Q: 2. Let X be continous with pdf f(x) = 1/x² if 1 < x < ∞, and 0 otherwise. (a) Does E(X) exist? (b)…

A:

Q: Let f(x) = (4 – 2x) f(x) has one critical value at A = %3D For x A, f(x) is Select an answer E…

A: Given that: f(x)=(4-2x)5

Q: What is the general solution of the given higher order DE xy" + x(y')² – y' = 0 ? Select the correct…

A:

Q: Er , √x (1) X(t+T) fx dx show that the Process * Elx X(t) = A cos(w.t + 6) in wide-sense stationary…

A:

Q:

A: We have given geometric distribution and two statistics associated with it and we have to check…

Q: (e) If f(x) is reducible over Q then f(x +a) : a E Z is reducible over Q.

A:

Q: Consider the function f(x) = ln(x)/x^5. f(x) has a critical number A = __? f"(A) = __? Thus we…

A:

Q: 1-e y = f(x) = ln fonksiyon eğrisinin x = 2 ve x = 4 apsisli noktaları 1+e-x arasındaki yayının…

A: The arc of the curve is given as:

Q: (c) f(x,u, v) = – log(uv - x" x) on dom f = {(x,u, v) | uv > x² x, u, v > 0}.

A: C.

Q: 15. If g(x) and h(x) are both antiderivatives of some func- tion f(x), then what can you say about…

A: Consider that gx and hx are both antiderivative of function fx. Find gx-hx.   Since gx and hx are…

Q: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)

A:

Q: 1. re (x, y, z) x). Ly). (z}} - *(*. y, z) . (x)S(x), ly), (z]} (x)E (x, y, z}

A: If x is element then it belong to set And {x} it will be subset of set

Q: If f(x) = x(e*+=') , then f'(x) = %3D %3D (A) (e² + æ³) æ(e*+z*-1) (B) (e" + 5æª) In(x) æ(e*+a*) (C)…

A: We have to find derivative of f(x).

Q: f(x)=x²-2x Sf(x)dx using four subintervals by on Estimate -1 d M4.

A: Given function is We divide the interval [-1,1] into four sub-intervals with length of each is…

Q: (a) Find the antiderivative F(x) of the function f(x) = x° – e* + e, that satisfies the initial…

A:

Q: Show that (0, 0) is a critical point of ƒ(x, y) = x2 + kxy + y2 no matter what value the constant k…

A:

Q: Let L(x) be the liberalization of f(x)=e^x at a=0 Use L(x) to find the approximate value of e.

A:

Q: a) Find the maximum percentage error in z if the percentage error in x is 1% and y is 2% given that…

A:

Q: Let f(x) = (3 – 4x)* f(x) has one critical value at A = For x A, f(x) is Select an answer

A:

Q: 2. Give an example of a regulated function f on [0, 1] such that f(x) > 0 for all æ e (0, 1), So…

A:

Q: a) z=-3x y² + sen(x²y) 2x c) z=-In (x y³) e) z = x²ln(2x³y) b) w=2xz-3e²xy d) z=2e²y sen(x) f) z=…

A:

Q: Determine the value of the Wronskian W (y1, Y2) of y" – 2y +1 = e2 (x +1) if x=1.3 by using…

A:

Q: a. The function f: RR given by f(x)=x² is twice continuously differentiable in R", and its Hessian…

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: If G(x) is an antiderivative of g(x) and F(x) = G(x)- 5, then F(x) is also an antiderivative of…

A: See below the answer

Q: The coefficient of correlation between X and Y is - and o = a, of = 4a, and %3D %3D ož = 114 where Z…

A: Given: Z=3X-4Y. The coefficient of correlation between X and Y is 13and σx2=a, σy2=4a,σz2=114

Q: 9. Find the critical points and classify these as local max, local min, saddle point, or "can't…

A: (f) . Given function psf(x,y,2 = (x2+2y2+322)e  (x2+y2+22)solution :-To find the critical pointsfx =…

Q: 2. Given f(x) = x' + ax² + bx has critical numbers at x=1 and x=3, find a and b. .2

A:

Q: If f(x) =x - r- 3x+6, what are the critical value(s) of f(x)? (a) x only (b) x=3 only (c) x=-,,x=ì,…

A: Consider the given fx=23x3-52x2-3x+6

Q: If f(x) = x(e*+) , then f'(x) = %3D (A) (e + x³) x(e²+x²-1) (B) (e" + 5x*) In(x) æ(c*+z*) (C) (e* +…

A: To find f'(x) for the given function

Q: - Use Euler's method to estimate y(3) given y(0) = 1, and y' = x -. Use steps of h = 1

A: use euler method for finding the y(3)

Q: Find the linearization L(x) of y = e3" ln(x) at a = 1. %3D L(x) = ||

A: See the details solution in the details solution

Q: (a) Find the antiderivative F(x) of the function f(x) = xe – e + e, that satisfies the initial value…

A:

Q: SSS zdV Q3: Evaluate E + y² + z² = 1 and x² + y² + z² = 4 in the upper where E lies between the…

A: We have to evaluate the integral ∭EzdV, where E lies between the spheres x2+y2+z2=1 and x2+y2+z2=4…

Q: 2. for the fumetion Fex) =x2 3x*+5X+4 3. E'a a) fx b) IniCrease, decrease C) mónimiun, mehimun(5, (^…

A:

Q: a'(t) = -x(t – 1), x(t) = 1 on [-1,0], is given by 1(t) = E(-1)* t – (k – 1))* k! for n-1<t <n, k=0

A: As per the question we are given the following first order time varient differential equation :…

Q: If f(x) - g(x) = 1, then f and g have the same antiderivative. %3D O True False

A:

Q: Lec 4.1: e Js Estimate with n Hhe aceuracy of 10t Brsection' Method and decidny applyning on b. De…

A: We can form a function f(x) for approximating square root of 5 then we can use bisection method.

Q: Ôz 12. If z = cos(x y)+ y cos x , where x=u +v and y=u-v use the chain rule to find and ди

A: Given: z=cosxy+ycosxx=u2+vy=u-v2 Recall the chain rule,  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u…

Q: 16. If f(x) = 5, (;e* G +5) dt -x, then the inflection point(s) of y = f(x) is(ar- %3D 3 A) x = 4…

A: f(x)=∫0x14t4+5dt-13x4

Q: 16. If x x y and y x z, then how is x proportionally related to z?

A:

Q: If we use a linear approximation of e- at a = 0 to approximate e-1/3, then we obtain: А. 4/3. В. 2/3…

A: The solution is given below

Q: se Euler method to compute ys for the DE yy'=2 x for y(1)=3

A: Euler's Method

Q: A company finds that its marginal revenue from the sale of the xth unit of its product is given by…

A: Solve  for total revenue function