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Q: Sinha Sechct) At

A:

Q: Give Three Functions  of Wronskian ?

A: To Give: Wronskian of three functions.   Wronskian:

Q: Show that cosh t + sinht = e and cosht - sinht = e. Hence, show that cosht- sinht=1. Deduce that…

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Q: Find the Gamma function of [(1) using definition

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Q: Evaluate in terms of beta function: (1 – +) dx. - O-8(금, 금) O-8(를, 승) O B)

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Q: With mean theorm, show that | cos x - cos y| < ]x – yl for all of x and y at R www.wwwnn

A: Mean Value theorem

Q: Stoke's theorem

A: We have to verify the Stoke's theorem for the given vector field. It is given that

Q: caleulate the

A: Given that: ∫dx15-4x-4x2

Q: Show that the function is continuous. (x) = 3x cos 3x

A: Show that the function is continuous. (x) = 3x cos 3x

Q: Which of the following decomp inside function) is/are correct ?

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Q: Prove that 1 3V2 dx < 3 + x (Hint: Theorem 5.9(ii) and carefully chosen functions should do the…

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Q: Evaluate by using definition Gamma Function 2

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Q: Comvert to retangular coodinates. Use exct values.

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Q: 1 Find the mean value over the interval [0,2n]. 4+cosx

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Q: Evaluate in terms of Beta Function: 20 ○ (1, 필) O-표8(1, 쫄) OB(1, ) OB(1, )

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Q: Sin x3D%=

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Q: Find HLK. Show your work.

A: Given, To find

Q: Find the mean value of over the interval [0,27] 4+ cosx

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Q: కషిద్టి చవీ / tangent s lope rosin (20) when Jot 5 2) 653 3. not of the above

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Q: State Fubini’s theorem.

A: Statement of Fubini's theorem

Q: 4. Verify the Mean Value Theorem for the function y=ln (2x + 3) in

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Q: Find all æ values on the graph of f(x) = 2x – 4 cos æ for 0 < a < 2n where the tangent line has…

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Q: Find the intervals on which f(x) = cos2 x on [−π, π] is increasing and decreasing.

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Q: (b) Use the definition to show that cosh(-x) = cosh(x). + e-(-x) cosh(-x) e-X + eX

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find the Laplace transform of tant. Show your full Solution.

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Q: Find the intervals of convexity/concavity of the functionf(x)=x−cosx.

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Q: Find y' by ased proportici Ln Xャ3

A: Taking natural log both side

Q: Use Simpson's Rule with ne4 to estimate Cos"xdx COSTX ☺ For ☺ an upper bound for the estimate. Hint:…

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Q: Prove the addition formula for cosh x given by cosh(x + y) = cosh x cosh y + sinh x sinh y.

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Q: Apply Gauss's theorem to evaluate. A

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Q: Find Maclaurin expression of f(x) = Cosh (x)

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Q: 6. Prove if the following function is differentiable y2 = (arctanx + 1)°*

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Q: 3:Use Gamma & Beta properties to evaluate : f (In x)³ dx

A: The gamma function is Γ(z)=∫0∞e-ttz-1dṭ The Gamma function is a non-integer generalization of the…

Q: Verify that the Mean Value Theorem (MVT) applies to the function f(x) = sin? x – cos x on the…

A: Mean Value theorem states that: f'(c)=f(b)-f(a)b-awhere f(x) is differentiable in (a,b).

Q: The derivative of the function f (x) = 3 sin“ x is Select one: O f'(x) = 12 cos³x O f'(x) = 12 sin³…

A: dsinxdx = cosx

Q: Find Fouri'sr trmsfarm of x+l= cos wut utt

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Q: Use the definition of the Gini Index to show G = 2(x-L(x))dx where L(x) is the Lorenz curve. Show…

A: &lt;math…

Q: Hiwiy Express the ballowsing functions by Palar equationft 2.

A: To change a rectangular equation to a polar equation just replace x with (r cos θ ) and y with  (r…

Q: : and degr S. F

A: We have to solve given problem:

Q: – one function from X into

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Q: 3:Use Gamma & Beta properties to evaluate : 2x¹e¹-* dx

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Q: Verify Lagrange's mean value theorem in f(x) = x²+2x-1 in (0,1)

A: We have ,  f(x) = x2 + 2x - 1    We know the , Lagrange's mean value theorem, If a function f is…

Q: dx хе

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Q: Using the integral definition of gamma function show that Γ(7) = 6 Γ(6)

A: The objective is to show that Γ7=6Γ6 using the integral definition of gamma function. Now,…

Q: If Z= tanh) show that: *

A: The given function is z=tanhyx We have to prove that x∂z∂x+y∂z∂y=0 ∂z∂x=The partial derivative of z…

Q: Show that cosh x> 1 + x² for all x.

A: comparison

Q: Verify Mean Value Theorem for the function 3x² – 4x + 5 in [-1,1] 1-tanx

A: Use mean value theorem

Q: by thể differen ntial equation on associated with this sy

A: In this question, the concept of Laplace Transform is applied. Laplace Transform The Laplace…

Q: ENRI Green's theorem to

A:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!