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Q: dx , if we let u =V 25 – x² , then udu = - xdx. (A True B False

A: Given query is to find statement is true or false.

Q: 10. If z = x + f(u), where u = xy, show that dz = x. х дх

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Q: (b) If z r+ry- y7, 1= u+ and y = 2uv, find: in terms of du %3D u and v.

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Q: ди ди ди for u = az Find p-q if p= x+ y+ z ,q = x + y + z ,r = = (V3,2,1). and ax' əy 9-r x + y - z…

A: Q3. Given that                                            u=p-qq-rp=x+y+zq=x+y+zr=x+y-zPoint, (x, y,…

Q: show that }I f,lm) Ck-m) 2.

A: For, ∑m=0kf1mf2k-m, substitute k-m=n or m=k-n: ∑m=0kf1mf2k-m=∑k-n=0kf1k-nf2k-k-n…

Q: (b) If V'u =0 for x2 0 and if u f(y) on x=0, Show that ,y): +(y-5)

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Q: Given, f(x, y, z) = xln(x?y)+ x*y – e a2. Compute fa, f, fry, fayz-

A: If f(x,y,z) is a multivariable function, then the variables x,y, and z are called the input of the…

Q: Prove that - V ニ soL 2m+V-V d. (1) m! Pempv +1) m!Pem+v +1) Atur m20 2. m26 2

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Q: Complete the proof that ZYXZ SUT. P Q R. U W Y

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Q: Prove VZEC, V2|z|>|Re z| +|Im z| + |Im z| Vze C,

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Q: 4 - If w = x + 2y + z? , x =, y= r2 + In(s) , and z = 2r aw find at the point (r, s) = (-8,4). as…

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Q: Show that if x', y are the deviation of the variables from their means, then x Yi r=1. Σ 2N - Ox Oy…

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Q: Complete the proof that AUVX ATWX. U V T. W

A: Given:  WX=VX and UX=TX. In △UVX and △TWX WX=VX                  (Given) UX=TX…

Q: 4. Given that T : R² → R* and is defined as T(x, y) = (x + a, y + b) . Prove that

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Q: 2. Find the correct value of c such that P (Z < c) = 0.4. %3D C =

A: According to the provided information, P(Z&lt;c) = 0.4

Q: 2- Let z=x+iy. Find a) Img(1/2) b) Re z c) Img (1/z')

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Q: If u * v = 2i - 3j + k, what is v * u?

A: As we know a×b = - b×a

Q: dz If z(x, y) = x²y, æ = 4, and y = u³ v², find du

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Q: x then ux is XX If u = V y %3D

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Q: For x,y E [0,1], prove that xy(1-x-y)≤1/27

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Q: EX: Verify that z= I+ V3i satis fies the 2. eq.

A: the given equation is z2-z+1=0 given the value of z is z=1+3i2 substitute the value of z in the…

Q: Prove or disprove: Vx € Q, Vy e Q, 3z E Q, (x < y) → (x < z< y).

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Q: s) Given u(r, s) =r2 - 2s2, wheter= and s = y? - r, compute for du

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Q: If u = (u, uz) and v = (V1, V2), how do you find u + v?

A: Given: u=(u1,u2)v=(v1,v2)

Q: Prove the following statements: d (a) [u(t) · v(t)] = u'(t) · v(t) + u(t) · v'(t). dt

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Q: prove. that s U. W V- W 1. U.r V.r

A: Using the vector triple product, it can be written that: a→×b→×c→=a→·c→b→-b→·c→a→. Using the scalar…

Q: Prove that c?p?-(jx² + jy²+jz³) is the invariant quantity equal to c?po?.

A: Consider the provided question,   Prove that c2ρ2-jx2+jy2+jz2 is the invariant quantity equal to…

Q: M. Uz Uz ů. cux w)= ) Vi V2 V3 %3D Wi Wz Wg Prove e 10:47

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Q: b) = f ) then prove that x ux + y uy + z uz = 0 u

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Q: Find and d?z and prove that 2 0²z IF 2 = f(xt ay) + F CX-ay) %3D

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Q: 1. If x, y, z E R, prove that (c) ||x| – |y|| < |x –yl. (d) \xy| < }(x² + y²)

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Q: of af 42. Assume that w = (х, у) — ху, and (х, у) ду dw dw Find and at ds

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Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

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Q: Prove that dv du 2 – u? + v² 18

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Q: 6. Use Green's Theorem to evaluate O (y* – xy?) dæ + (2 – a*) dy where C is shown below. y -2 ² +y²…

A: Green's theorem

Q: For x, y E [0, 1], prove that 1 xy(1 – x – y) < 27

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Q: Q₂. if z=f(x+ct) + g(x-(t) then show that C²Z = Ztt XX

A: Given function: z=fx+ct+gx-ct We have to prove that, c2zxx=ztt. We know that, daxndx=anxn-1

Q: Q: If u =f(x² +2yz, y² + 2=x)Prove that (y-ax

A: Step by step compute the derivative with respect to each variable x,y or z. Then substitute it in…

Q: 21. Find af and of if f(x,4)= 3x" +2xy+ Sy , x= 4v? + Bn", and u 2v-w? Vour %3D 4= 2v-w? Vour av…

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Q: (b) Let h(x, y, z) = x?y+ yz?, where a = u + v, y = u – v and z = -u. Calculate and ди dv

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Q: If E?uz = x² and h = 1, then find ux. %3D

A: The objective is to find ux. Given information is: E2ux=x2, and h=1.

Q: Reorder the form of the following question. 2%3D4 TT" f(z, 4, 2) dæ dydz. y=D0 f(x, y, z) dz dy dz.

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Q: Q/Find af/ax and af/ay xy Iny

A: The given function is fx,y=exylny To find: ∂f∂x and ∂f∂y

Q: P:(A UB) cB Q :AC(A nB) Q => P I have to prove that p=>Qond that

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Q: Question dz If z(x, y) = x²y, x = ", and y = u'v², find

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Q: Let f(x, y) = x² + y2 + 2x + 4 and P,(-1,0) then Vfle, is i – j. True False

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Q: If f(x, y, z) = In(2 + x² – 2y² – 3z), 7 =, then Duf(2, –1, 1) = - A) * V3 B) 11 C) V3 D) E)

A: The given function is:    f(x,y,z)=ln2+x2-2y2-3z

Q: 4 - If w = x+ 2y + z? , x= , y =r2 + In(s) , and y = r2 + In(s) , and z = 2r aw find at the point…

A: Using chain rule the given question has been solved in step 2.

Q: Given f(u, v), where u = x² y, v = xy? If at the point (2,3), f, = 4, fm = 3, fm = 5, ƒ, = 1, fm =6.…

A: Given; u=x2y, v=xy2

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.