Ex(ia)g prove or dis prove that Ris equivalance relation on x iff Rtis equivalene relakion ony

Q: Let f(x+y)-(x)(y) for all x, y e R and suppose that fis differentiable at x = 0.Show that fis…

A:

Q: Define g : R →R x sin (1/x), g(x) = 10, x # 0 x = 0. Explain why g is continuous at 0; in…

A:

Q: (b) Is the function h(u, v) = cos(u) + enu +sinh(u²)+ vv + enu , Where n=4. Is h is continuous? In…

A: (b) is the given function hu,v=cosu+enu+sinhu2+v+enu , where n=4 continuous? if yes then find the…

Q: Let f(x) = (1+sin?x) then Limit of f(x) approached to zero equal to : %3D as x Awww

A: Given: fx=1+sin2xx2 For evaluating given limit, we put x=0 in given expression

Q: (3) that кете Use Riemann's Criterion to prove the constant function f. R > R = k given by f(x) 4…

A:

Q: 1. Consider the function: f on [0, 1] by 7 if r1 f(x) |0 if 1 0, 1]. Prove that f is Riemann…

A: To prove that f is not continuous but Riemann integrable

Q: Define fi z-> 2 xZ by Ala)l (2,72t1) if xis even 18,0) if t is odd a) Is f injective 2? b) Is f…

A: We have f:Z→z×z Such that fx=x,x+1     if x is evenx,0          if x is odd

Q: Let G(x) = tan 9t dt. In order to use the Fundamental Theorem of Calculus (Part 2), G(x) needs to be…

A: For the following integral,

Q: Consider a continuons fimetion f(x) on [1, 4] that is dif- ferentiable on (1, 4). If f(1) = 10 and…

A:

Q: Hello want to ask how to do this question: Using the definition of integrability or integral…

A:

Q: Let ƒ(x, y) =(x2-y2)/(x2+y2)  for(x, y) ≠ (0, 0). Is it possible to define ƒ(0, 0) in a way that…

A:

Q: The area of the region between the graphs of y = r and y = -x from x = -1 to r = 0 is .2 %3D %3D…

A:

Q: 1 Let f (x, y) =x²y*sin (- x²+y* when (x, y) ± (0,0) and f (0,0) =0. determine if f is continuous in…

A: We have to show given function is continuous at origin

Q: f(x) is increasing and bounded on [0, 1], then f(x) is Riemann-integrable on [0, 1].

A:

Q: sho w that fQ) = x xE To,1] is Riemann integrable amm

A: The given function is: fx=x3, x∈0,1

Q: Show that limit t  appraoaches infinity  integral -t  to t  x dx =0  This shows that we can’t define…

A:

Q: 20. Use Simpsons' rule to numerically integrate for the n = 6, case f(x) = x on the unit interval,…

A: Using Simpson's rule to find integration Unit interval means [0,1]

Q: Let a, b, c, d be numbers and f(x,y) be any function. Then . f(x, y) dxdy This statement is --- --…

A:

Q: Let f(x) = x² sin – if x # 0 and f(0) = 0. Then f Reimann Integrable O False True

A: Theorem : Continuity implies integrability :: If f :B→ℝ be a continuous function where B⊂ℝ is…

Q: 4. Express the limit as a definite integral and then evaluate the integral using the Fundamental…

A:

Q: กำหนดให้ f(x, y) = xy cos.x x² +3y²

A:

Q: Show that the function f defined on [0, 1]'by the conditions 1 f(x)=2rx when 7=1, 2, 3,...... És…

A:

Q: To prove this function to be Reiman Integrable * 4/4 { 0 ifx= 1 3 if x + 1 Let f : [0, 3] → R be…

A:

Q: Determine where f(x) = - is differentiable. sin xcos x пл 2in = 0, ± 1, ±2, .. Ox = na, n = 0, ± 1,…

A: Given function is: fx=7sinxcosx To find the points where the function is differentiable.

Q: Evaluate function given assuming ƒ is integrable on [a, b].

A: We have to calculate,∫abf(x)dx+∫baf(x)dx = ?            ...................(1)As function f(x) is…

Q: Express the limit limE (7(;)* – 5(x; )*)Aæ; - i=1 over [4, 6| as an integral. Provide a, b and f(x)…

A:

Q: Prove Fermat’s Theorem for the case in which f has a localminimum at c .

A: It is given that f has a local minimum value at c. Thus, by the concept of local minimum, fc≤fx when…

Q: Which of the following is true about f(z) = z+ iz %3D 22 ختر أحد الخيارات to Neither Continuous nor…

A: f(z) = z+ iz / z2 f(z) = 1+i / z     We should here note that function 1/z is continuous everywhere…

Q: Let f(x, y) = Scosy.sinx, x # 0 cosy, x = 0 Is f continuous at (0,0)? Is ƒ continuous everywhere?

A: We have to check whether the given function is continuous at x = 0 or not. Also, check whether it is…

Q: 3. Define f:R –→ R by ƒ (x) = sin (1/x) if x # 0 and f (0) = 0. (a) Show that fis not continuous at…

A:

Q: ve that the Bessel functionm generating funchion ie too

A: The aim is to show that∑n=-∞∞Jn(x)tn=ex2t-1t The approach for this proof is, Take,…

Q: Let f : [a, b] R be a function defined by 0if rEQ . if r¢Q f(x) = %3D Show that f is not Riemann…

A:

Q: xy cos.x f(x, y) =+3y²

A:

Q: The improper integral f(x)dx can be written as lim f(x)dx + lim_f," f(x)dx . ... W→ー0 w+00 If f(x) =…

A:

Q: Let ƒ be a Riemann integrable function on [0, 1]. n (i). Let g be in (0, 1). Find lim La n→∞…

A:

Q: Let f(r. y) = * if (1, y) # (0,0) if (1, y) = (0,0) Show that af/ðr and af /ðy exists at (0,0) but f…

A:

Q: (b) Let f be a function defined by 1 if x e Qn [a,b] f(x) = - |-1 if x€ (÷) n [a, b]. Show that fis…

A: we are given that f(x)=1   if x∈Q∩[a,b]-1 if x∈(RQ)∩[a,b] To prove f is not Riemann-integrable  on…

Q: Is the function h(u, v) = cos(u) + emu +sinh(u?)+ vv + emu , Where n=6. Is h is continuous? In case…

A:

Q: To prove this function to be Reiman Integrable 0/4 {: 0 if0<x < 1 4 if 1<x < 4 Let f : [0,4] → R be…

A: Given f:0,4→R defined by fx=0    if 0≤x≤14    if 1&lt;x≤4 We use here a theorem which states that…

Q: true or false  If f is continuous on [a, b], then f has an antiderivative on [a, b]r

A:

Q: Evaluate in terms of Gamma function: y^5√(b^2 – y^2) dy LIMIT: 0 to b

A: The given data is: y5b2-y2 dy limit is 0 to b To evaluate in terms of Gamma function.

Q: f(x, y) = ´x cos(y) + y(e² − 1) xy 0 x=0 x = 0.

A: Given function is fx,y=xcosy+yex-1xy,     x≠00,                                     x=0. To prove:…

Q: use Greens Theorem to evaluate . cosy dx + (xy- x siny)dy Ewhere C is the bounday of the y Jx,…

A: We have to evaluate given integral using Green's theorem.

Q: Use : f(z)-L im $(Z+Az)-f(z) AZ to Prave that -1 when w- I Zキ0

A: Here definition of derivative is given in terms of limit. We have to find the derivative of the…

Q: Use the Mean Value Theorem to prove that, for all x, y € IR, cos x - cos y ≤|x-y.

A:

Q: II. Find all values of a and b that make -а - х, f(x) = {bx² + 1, Vx + b, x<-2 -2 sx<1 x21…

A:

Q: continuous on ( UOUS O

A: Given function is: fx=3x+6a  ;  if x&lt;-33ax-7b   ;   if-3≤x≤3x-12b   ;    if 3&lt;x We have to…

Q: True o false ? If fand g g are Continuous on faib I, then

A: Please see the answer below.

Q: ) Denote the number of derangements of {1, 2,..., n} by Dn. Using the formula for the number of the…

A: Given Dn be number of derangements of 1,2,…,n. Derangements is number of permutation of n objects in…

Q: (5) Suppose that fis continuous on [a, b]- f(x) ≥ 0 Vx = [a,b] and [f(x)dx = 0. Prove that f(x) = 0…

A: