Suppose E, F C S with Pr[E] = 0.2, Pr[F] = 0.5 and Pr[E' n F] = 0.45. What is Pr[E\F]?

Q: Find the smallest integer n to guarantee that the error in using Tn to approximate | e dx is e less…

A: The integral is ∫01ex2dx  The error of Tn is obtained by the formula is E=-b-a212n2f''c We want…

Q: dy +y = zy dr

A: Given equation is: xdydx+y=xy3

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Q: e*(1-cos(x)) Exercise: Evaluate S dx.

A: Now evaluate the integral, ∫0∞ex(1-cos(x))xdx Take the minus as outside and it is concluded as…

Q: 4.62. Evaluate the derivative of the Gamma function and see dT'(x) r'(x) = dx ' (In t)e"'dt

A: To differentiate the gamma function:         Γ(x) = ∫0∞tx-1e-tdt Integral definition of gamma…

Q: If X has an ex ponential (A) PDF, what is the PDF of W = X² ?

A: 4. Given information: The random variable X has exponential distribution with . The probability…

Q: Prove that sinh−1 t = ln(t + √t2 + 1 ).

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Q: d Prove In Jax| dx In x for any constant a. dx

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Q: Drove that 3 e dx converges to 9 3e

A: Explanation and solutions is given below.....

Q: Find the linear approximation of f(x) = ln x at 1 and use it to estimate ln(1.33). L(x) In(1.33) =

A: Given : fx = lnx

Q: (b) Evaluate 1 dx using Romberg's S. 1 + x2 hence obtain an approximate value of T.

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0. ƒ(x) has a root in [0,1]. If we…

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Q: dy log x If xY = ex-Y, prove that %3D dx (1+ logx)?

A: Introduction :

Q: f(x, y) = 1/(xy), then the marginal pdf of X is (log x)/y. Is this statement True/False?

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Q: Calculate the derivative e10x de L9 In (t)dt using Part 2 of the Fundamental Theorem of Calculus.…

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Q: If s = f(t) denotes the position of a particle at time t, the derivative f'(c) is the of the…

A: Solution:Given      If s=f(t) denotes the position of a particle at time t, the derivative f'(c) is…

Q: If X is an exponential RV with parameter A, find the PDF of Y = -14 In(X). 2

A: Given information: If X is an Exponential random variable with parameter λ. The pdf of X is,…

Q: Can you help me with this problem step by step?

A: Given that

Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate In(1.18). L(x) =…

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Q: find the general slühion with real values fn +y(H)=0

A: I am consedering y4(t) to be (y'(t))4

Q: .2 -dædy In (x) ey

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Q: Use the Simpson's rule to estimate S, ex dx with n = 4

A: Consider the given integral ∫12ex2dx with n = 4. Simpson's rule is,…

Q: dy dr

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Q: Prove that coshz =log ztv= {Hint : cosh z =e} 2.

A: Use the hint and prove this.

Q: 1. dx Evaluate 0, et +e-*

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Q: Use the Beta and gamma function -1 n! 1- Prove that x™(ln x)"dx (m+1)n+1

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Q: Find values of p for which integral diverges. dx x(In x)"

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Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate ln(1.34). L(x) =…

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Q: Evaluate the function: ( e* +1 dx et

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Q: 4. Compute dx S in two ways and verify that the answers agree.

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Q: What is the first derivative of s(r) = log, sin z 712+8z+2 Provide your answer below: s'(x) =]

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Q: The value of n when integrating the following function using Simpson's method is: [2²/ dx h = 0.2 >

A: solution is given below

Q: Find the linear approximation of f(x)=ln x at x=1 and use it to estimate ln(1.24). L(x)=?…

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Q: if p> 1, (diverges; if p <1. 0o dx Prove that f p- 1 хР 1 Hence evaluate: dx. x6

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Q: Find the differential of the function. = e dy =

A: y= e^(2x) dy = 2 e^(2x) dx

Q: Suppose g(x) = = A, and f' (1) = B. Find the derivative In(In(In(f(x)))), %3D f(1) = dg dx \x=1…

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Q: Use the Simpson's rule to estimate e**dx with n = 4

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Q: Find the indefinite integral x2e +e² dx.

A: The given indefinite integral is: I=∫x2e+ex dx

Q: y²

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Q: Compute dx in two ways and verify that the answers agree.

A: Assume the given integral be I. I can be integrated via trigonometric substitution by substituting…

Q: Show that the following functions all grow at the same rate using properties as x co: fi(x) = x°,…

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Q: e2: S dx 1+ex

A: Given the integral ∫e2x1+ex dx u = 1+ex  ⇒ ex = u - 1 du = ex dx By substitution method, I=∫e2x1+ex…

Q: The following differential is separable: dr = b(cosxdr + rsinxdx) true or false?

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Q: Using Simpson's (1/3) rule with h = 1, evaluate the integral: 7 = f x² logx dx 3

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Q: prove using the IVT. e^x + ln x = 0 has a solution.

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Q: 10. Compute the central difference approximations of O(h^4 ) for the first derivative of y =cos(x) +…

A: Solution is below

Q: 4. Express the integral e-t tổ dt in terms of gamma function.

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Q: Find 뿐 for the ry – ln(xy) = 1 0 뽈 ㅇ-볼 O 래 ㅇ-픕 following:

A: The given expression is xy-lnxy=1 we have to find dydx use the derivative formulas, ddxx=1…

Q: Find the length of the curve y = ln x from x = 1 to x = e.

A: Given:Find the length of the curve y = ln x from x = 1 to x = e.

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)? dx y logy x

A: