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Q: 1 Let f (x,y) =In Then f (1, – 1) =... 3x2+4y3 XX

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Q: dt converges. There is no value of r such that (3t)-" 14.

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Q: sn'x プェ Sec'x-1 from [o, of 2.

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Q: Sin (n+))x Conv. unif nナノ on Prablem (5) Is the senies

A: The given series is: ∑n=1∞sinn+1xn+1 The given interval is: 0,π

Q: Q3: Prove that Σ(y₁ - y) = 0 AND Σfi(y₁ - y) = 0

A: The question is about proving given equation. To prove : ∑ ( yi - y¯ ) = 0∑ fi ( yi - y¯ ) = 0

Q: 2. Show that by using MEAN VALUE THEOREM. u-v n >0 1+v2 3 <tan- < and deduce that 25 ww 4

A: First we have to show that v-u1+v2&lt;tan-1v-tan-1u&lt;v-u1+u2 where 0&lt;u&lt;v. Then we will show…

Q: dn-1 for all n E Z with n > 2. Prove that for a 2. Let d = 2, and d, neN, d, =. %3D %3D %3D

A: Mathematical Induction is a special way of proving things. It has only 3 steps: Step 1: Show it is…

Q: 3. Determine a and b for Y X1 and Y2aX bX2 such that EX1 EX2}= 0, Var(X) Var(X2) Var(Yi) Var(2) 1,…

A: The provided information is:

Q: Q4: 16 u. nin N, then 5 bounded fo belongs t and infinum

A: We define a subsequence  an = Sin(pi/2) + (-1)n = 1 + (-1)n . So, a2n = 2 and a2n - 1 = 0.

Q: 2. given that y = 0 at r=1

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Q: 18 For which numbers a does x,+, = a{x,– x) converge to x* = (a – 1)/a?

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Q: 15. Solve Orx + Pyy 0, -a < x < a, 0 < y < ∞, 8o, 0 < |x| < a, Oy (x, 0) = 0, || а. $ (x, y) → 0…

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Q: If X is uniform in the interval [-3,3] compute X(i.e. E{X}) and o² (i.e.E{(X-X)²}).

A: Given that X ~ U[-3,3] to find mean and variance

Q: @) 2) Fs of (x) = -PFC (Psy) -} [ If f (x,y) → as 6004X proof. (H-w.) then в

A: Introduction: The Fourier sine and cosine transforms are variations of the Fourier rework that do…

Q: On which interval is the IVP (x sin x)y' + 2y = x +1, y(-5) = 2 guaranteed to have a unique…

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Q: ー28- Sa Oclumina f dz sabishy cauchy- Reimon quakir f andlgove @ frz= J-2xy ti C-Xyz] +z* @ f(2)=…

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Q: The Ideal Gas Law states that PV = nRT where P is pressure, V is volume, n is the number of moles of…

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Q: If X1, Y1, are two positive unequal numbers and Xn = (xn– 1+ Yn – 1) and y,= Vx – 1 Yn –1 V n 2 2.…

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Q: Let X and Y be independent and distributed as N(u, 1). Is T = X-Y sufficient?

A: According to factorization theorem, If the likelihood function L(x,θ) can be expressed in the form…

Q: Show that the series n=0 xn cos(nx) x² +n³ + 1 defines a differentiable function g(x) for x in [-1,…

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Q: Suppose that a manufacturer is testing one of its machines to make sure that the machine is…

A: From the provided information, The hypotheses are as follow: H0: µ = 15 Ha: µ &gt; 15 The p value =…

Q: The evaluation of S V1 + tan2x dx is C In(V2) +1 In(vZ+1) C In(vZ-1) O-In(vZ+1)

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Q: A random process is dėji process and a >0 is a constant. Find the PSD of Y (t) in terms of the…

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Q: he IVP d's (p² – 121) dp1 d's ds + s 1 = sin(p) dp3 p2 +1 dp s(7) = -994 ds = 19 dp l7 d's = 4 dp2…

A: Given the IVF (p2-121)d4sdp4+p4d3sdp3+1p2+1dsdp+s = sin(p)s(7)=-994[dsdp]7=19[d2sdp2]7=4[d3sdp3]7=10…

Q: 2. A stock market trader buys 100 shares of stock A and 200 shares of stock B. Let X and Y be the…

A: Step 1: It is given that trader buys 100 shares of stock A and 200 shares of stock B. From the…

Q: 2 (b) S(2 + tan (0))do (c) S 2'(1 + 5')dt

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Q: Fird XCK) is X(2) = 2くz-)(マ-3) Ans; SC) ャu(k)+と)uck)

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Q: az Find for z = x²y°e®Y dx

A: The given function z is zx,y=x2y2exy We have to find the partial derivative of z with respect to x.

Q: <x<) for f(x) = x².cos x³ 0.235 O 0.304 O 0.908 O 0.413 O 0.678 O 0.112 O 0.503 O 0.774 O Find the…

A: We need to find tge probability P(0 &lt;x &lt;π/3) for f(x) = x2 cos x3

Q: Proof by contrapositive that for xy EZ, if xy is even then either x or y is even.

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Q: In Exercises 5–12, find and sketch the domain for each function

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Q: Show for Re(z) > 1 ex – 1 dr = T(z)5(2). et – 1

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Q: 4.5.1 Y is a continuous uniform (1,5) ran- dom variable. (a) What is PY >EY]]? (b) What is P[Y <Var…

A: A random variable Y is said to have continuous uniform distribution over an interval (a,b),(i.e…

Q: If utt 4ura u(x, 0) = e", u4(x, 0) = 0, u, Ux → 0 as x → ∞, then u e* cosh(2t) O e2 cosh(4t) O e2¤…

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Q: Ôz Ôz If Z= tan"'(2) -= 0 show that : *-+ y ôx ôy

A: Let us consider function z=f(x,y) Where f is function of x,y. ∂z∂x represents partial derivative of…

Q: at to a o and terms of power senes' and opa apen n nlervas f Converganca dt t t. 2.

A: Given The given integral is ft=∫t1+t4dt Taylor series for fx=1+x+x2+x3+···=∑n=0∞xn, where x&lt;1. If…

Q: дz (B)If Z = f(x, y), x= s² - t², y = 2st. Prove that s მs 2 (s² + t²) of əx

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Q: We hae a theorem that offers conditions when the IVP: x'- f(t, x), x(to) = X , has a unique…

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Q: 2s If F (s) = (s+1)2 then

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Q: 21. xª sen z dz -z' cos z + 3z² sen z + 6z cos z 6 sen z + C %3D

A: see below the answer

Q: 4) Fund the interval of x-value on which the Carve is Con Cave up and Con Cave dawn 3 fex) = +x-3X

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Q: 1 Let f (x,y)=In . Then f „(1, – 1) =...... 3x²+4y3 XX

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Q: n²sinx Show that g„(x) converges uniformly to x e [1,5]. 1+ n²x

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Q: 1. Let x (x,) E l. Find x if 11-- a. x = 2 %3D

A: This is a question of functional analysis in lp space.

Q: Find y' if y= In coshv tanh v. y =sech v-2tanh v O None of the above O Option 4 y=tanh'y y'=tanhv –…

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Q: P(x) 1 2 5 6 IRound to fonur darimal nlarae ae neerlad 4)

A: here use binomial distribution with parameter p = 0.7 and n =6 for binomial theorem ,…

Q: x2/3 is (are) The critical number(s) of f(x x – 1

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Q: 3) Find the deri vative of cscC (x) (xf3)' X4

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Q: c- Verify Clairaut’s Therom f(s,t) = s²t + In(t²-s)

A: In the question it is asked to verify Clairaut's theorem for the following function given in…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: