If the pdf of a measurement error X is f(x)= .Se -00

Q: Match each function with its derivative. y dy dx ха X a. cos x b. In a • a* ✓ax C. sin x - ✓sin x d.…

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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: Find the value of the constant C for which the integral 3 3C dx x + 25 X + 5 converges. C =

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Q: Find the value of the derivative y′(x) at x=0 for the function given by ey+xy=e.

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Q: In each of the following cases calculate the indicated derivatives, justifying all opera- tions. (a)…

A: This is a problem related to antiderivative of the function. Please follow the procedure given…

Q: 17. Find the values of p for which the integral So dx converges. OpE (-1,1) Op21 Op 1 Opsl

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Q: For what value of a, b > 0 is the following integral convergent. dx . x*(1+x*) a + b 1 O a, b>1

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Q: If x = tan - log y a d'y dy Show that (1+x²)- +(2x- a)-0 dx dx?

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Q: Find the linear approximation of f(x) = lnx at x = 1 and use it to estimate ln(1.02). L(x) =…

A: Given that: f(x)=lnx

Q: Q8. Using 1/3 Simpson's rule with h = 0.1 estimate (x - 3x2 + 2). dx

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Q: |If f(x) = a4 is the parent cubic function, prove that the AVERAGE rate of change of f(x) over the…

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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: Use Euler's method to make the graph of the following functions on the given interval. a) dx/dt = t…

A: Introduction: The Euler's method is a basic and numerical method to approximate an initial value…

Q: If; of t = x then at t=1 is (Note that these functions in N) dx

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Q: Solve th D.E using Exact dx +(x² +3y* )dy

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Q: Evaluate the second derivative of e22.1.png acos(b/x) f(x) x2 if a = 323 and b = 0.5 at x = 3 using…

A: Given function is f(x)=323cos0.5xx2 Step value is ∆x=0.1

Q: The distributional second derivative of u(x) = |x|, Vx R is given by O бо 0-80 O 0. 200

A: To find the distributional second derivative of ux=x, ∀x∈R.

Q: Consider and solve the initial value problem of a new form of life discovered on a distant planet.…

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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: Find the slope of the tangent line to the graph of x²-Iny=0 at x=2 O None of these O 4e4 O e4 O 4

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Q: (x' Log, x dx O For what values of p does al converge?

A: SOLUTION-

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: Find e dx approximately using Simpsons rule with n 10.

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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: How large should n be to guarantee that the Simpson's Rule approximation to dx is accurate to within…

A: Given:  ∫017ex2dx             where f(x)=7ex2 and a=0 , b=1.

Q: 1. If F(x)= = cos a sin r (√t-1)' dt, find F'(x).

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Q: | 17e dx is accurate to within 0.0001? How large should n be to guarantee that the Simpson's Rule…

A: let f(x)=17ex2 differentiating four times to get fiv(x) because the fourth derivative will be non…

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: 1+e* dx diverges 0.

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Q: 大 If x < 0, which of the following has the derivative 1 dy (1 – a)Va - 2a =? dx |3|

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Q: Consider and solve the initial value problem of a new form of life discovered on a distant planet.…

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Q: Let e 2* = 2 find dy dx at x = 1

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Q: find the antiderivative of the following derivative  dy/dx= x^-2 e^-1/x

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Q: The pdf of a continuous RV X is given by f(x) = cos(Ax)+ 10, where x E [0, -1. Find the value 2A of…

A: Given density function of the random variable X is, f(x)=cos(Ax)+10, x∈0,π2A The value of A is…

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: Evaluate the derivative of e22.1.png acos(b/x) COS f(x) = x2 if a = 71 and b = 0.5 at x = 2 using…

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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: The equation of the tangent line to the graph of f(x)=ln(x) at x=e^−1 is given by y=mx+b for m =…

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

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Q: 1. Find the average rate of change in y with respect to x over the interval [1, 7]. 2. Use the…

A: Given that: The function is f(x) = 4x -3 .

Q: Find the derivative of the following function. y= In (In (4x)) dy dx

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Q: S() dt, where f is a continuous function, find f(4). (c) A 10 ft ladder rests against a vertical…

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Q: xy = In (2y) – e

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Q: The derivative of y with respect to given a = 1 is Onone of the choices O y = yx³-1 O V = 0 = = 9 *…

A: I have stated the used formula in the solution

Q: 2. If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y.

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Q: If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y. TRUE or FALSE ?

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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.

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.