nx 4. Let fn(x) = 1+7²², x € R. Prove that fn → 0 pointwise on R, then check whether fn → 0 uniformly or not on [0, 1]

Q: 'he function f: E → R is uniformly continuous if

A: We have to find the answer using the definition of uniform continuity.

Q: EXvyP(x, y) is true when there is an x for which P(x, y) is true for every y. A True B False

A:

Q: f:1→1, (f(a)), =1 if n = 0 = n-a, – 1 if n= 0 (f(b)), = b, find b2010 - %3D

A: Given: f(a)n=1 if n=0nan-1 if n≠0and f(b)n=bn To find: b2010=?

Q: Exercise 4: How many functions f exist such that f'(x) = 3x2 - 6r +3, and (1,-2) is a point of…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 4. Prove that f(x, y, z) = 2 - 1 x² + y² is continuous in all its domain.

A:

Q: x and y are independent and uniform in the interval (0, a). Find the p.d.f. of (a) x/y, (b) y/(x+y),…

A: The objective of the question is to find the probability density function (pdf) of three different…

Q: If f(x, y) = In (2x-3y), then find of ||

A: We can solve this problem using partial derivatives.

Q: Evaluate * Vx² – 1 dx.

A: Given,  ∫ x2-1x2dx

Q: Find of z = In(xy)

A: Given,Z=ln(xy)differentiating both the sides partially w.r.t. x∂z∂x=1xyy1∂z∂x=1xagain differntiating…

Q: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

A:

Q: Determine fr and fy from f(x, y) = x³ + x²y + xy² + y³ ○ fx = x + xy, fy = x + 2xy ○ fx = x² + xy,…

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Q: -If F= 3xyz' i+ 4x'y} – xyzk the find V (V-F) and V × (V × F) at (– 1,2, 1). Also verify that V…

A:

Q: Let X~U (0,0), then P(X > X²) is

A: Given that X~U0,θ fx=1θ-0=1θ, 0≤X≤θ

Q: Prove: If f1, f2 € R(a) on [a, b] with fi < f2, then ' fi da < s' fz da

A:

Q: Find the aven bounded by y=x and y =x+2

A: First draw the graph of the function and find the intersection point of the graph:

Q: Decide whether or not the real function In (eon 2) I+0, = (1) 1= 0, is continuous at r = 0.

A: The given function is fx=ln cos2x2x2     if  x≠0-1                if  x=0. Compute the limit…

Q: Evaluate fv*+1dx x2 A. 를 (1 +즐)를 -를 (1+ 즐)를 :. 를 (1-즐)를 -를 (1-2)를 + C + C + C D. + C Evaluate the…

A:

Q: Let f: Nx N → Z defined by f(n, m) = n − m² 1. Find f({(0, 0), (1,0), (0, 1), (1, 1)}) 2. find…

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Q: Let X=(1,0, – 1, - /2)'. Then, ||X||, =| Select one: а. -1- V3 b. -V3 O C. 2 +/2 d. -V2

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Q: of of and ду Find f(x,y) = Vx + 3y?

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Q: Let f (x, y) = Vy – 2x Evaluate f(3, 10)

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Q: prove that ਰ Apply the calculus of residues to dx (1 + x²)² - π 4 .

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Q: Find all the strictly monotonic functions f: R→R such that f(x + f(y)) = f(x) + y, for all z, y € R.…

A: a. Consider the given condition, fx+fy=fx+y, for all x,y∈ℝ. Here we need to find the strictly…

Q: Ja - 2, x < 0, a+ 2, x20 9. Let f: R R be defined by f (x) = then f-(]1, 3() (the inverse image of…

A:

Q: Let X=(1,0, – 1, - V2). Then, ||X||1= Select one: a. -1-V3 b. C. -/3 o d. 2+V2

A:

Q: By using the substitution u = 4x + 1, evaluate (4х + 1) dx +x + k 4x? + x + k (4x + 1)² + k x' + x +…

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Q: aF O F2 aF, If F = F,I+Fj +F,k then prove that div F = + ду

A:

Q: Let f(r, y) = In (z³y) (1,3) = 3. then Select one: O True O False

A:

Q: d Suppose X₁~N (0,1). Prove that X0

A: Given,

Q: Letf (x, z) = 3x² – 12x + 3z² – In(z). Find the value of x* and z* where a min/max will occur. x*=2,…

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Q: Let X=(1,0, – 1,-/2)'. Then, ||X||2 = Select one:

A:

Q: 9. Find div F if F(x, y, z) = x²yi + xyzj - x²y²k. A. 2xy + yz - 2xy² B. x² + xy C. 2xy - xz D. 2xy…

A: