Find the linear approximation of f (x) = ln e at L() In(1.42) 1 and use it to estimate ln(1.42) Preview syntax error Preview

Q: Determine if the improper integral converges or diverges: 1 dx. 1+x²

A: Our Aim is to determine whether the improper integral given below converges or diverges∫0∞11+x2 -(i)

Q: Explain, in terms of linear approximations, why the  approximation is reasonable. ln 1.05 = 0.05…

A: Given: (1.01)6=1.06

Q: Using integration, derive the Laplace transform of: * L(sinh at)

A: This is a problem related to integration. based on the general formula and concept we will answer…

Q: 6. Evaluate: dædy Hint: Use dydx as order of integration.

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Q: Use linear approximation to estimate ln(.99)

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Q: Evaluate the qwen Detinite Integra ax(7-x²)* dx 2X

A: From the given integration: I=∫-3-22x7-x23dx.....(1) Using the substitution method to calculate the…

Q: 5. Use Linear Approximation to estimate e(-0.01). Provide your answer in 2 decimal places. Do not…

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Q: Evaluate the double integration: e²x e dxdy

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: dx x2 – 1

A: Given: ∫02xx2-1dx

Q: Would you use numerical integration to evaluate. Explain.

A: We have given a definite integral;

Q: Let f(x) = x sin(2 x). Find its average value for 0sxs/2.

A: Given the query is to find the average value of function over the interval [0,π/2].

Q: 2. (a). Use linear approximation to estimate ln 1.03. (b). Compute the percent error in your…

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Q: b What value of a and b that minimize the integral : (x* – 2x²) dx a (Hint: Where is the integrand…

A: We have to find the value of a and b

Q: use integration by parts to establish the reductionformula.

A: Integration by part formula: ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: If the integral diverges, indicate that using the checkbox. 6 dx The integral diverges x(x + 1)

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Q: Calculate the value of the integral dx to show that it is convergent. Then, use this result and the…

A: The given integral,∫1∞1x2dx and ∫1∞x2x4+x2+1dx

Q: Determine whether the improper integral diverges or converges. 1 dx e2x + e-2x

A: Evaluate integral,

Q: -Ixl dx Find the value of the integral and determine whether it is divergent or convergent

A: The given integral is ∫-∞∞e-xdx. Calculate the value of integral and determine whether it is…

Q: Make an octave code to integrate ex with respect to dx from 0 to 1, by Simpson’s ⅓ rule. Divide the…

A: Equation is f(x)=exThe value of the table for x and y x 0 0.25 0.5 0.75 1 y 1 1.284 1.6487…

Q: Evaluate the integral if it converges. Enter the exact answer, or enter na if it diverges. +00 -dx =…

A: Let I is the value of given Integral.

Q: Determine whether dx is convergent or divergent. If it is convergent evaluate the integral Vx 3. 4…

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Q: The integral of ƒ In(ln(x))dx can not be expressed as a finite sum of functions. What do we call…

A: It is called as non elementary integral

Q: 4. Use the definition of integration to find (1+2x' ) dx , that is find lim f(x; )Ax

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Q: в) (2.001)5 (b) у9999

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Q: Use a linear approximation (or differentials) to estimate the given number. Consider the linear…

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Q: Determine if the integral converges or diverges by comparison.

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Q: 5x

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Q: CK Show whye* dx does or does not converge.

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Q: 2. Integrate the following function (a) analytically 3. I- fxe2* dx and numerically using n = 4 (b)…

A: First determine the integral using integration formula's. Then use the formula of Trapezoidal and…

Q: 12. Approximate So dx with adaptive quadrature, simpson's rule, and Romberg integration

A: Given data I=∫01exx13dx

Q: Estimate the ln (1,1) and sec (0,1) using a linear approximation and without using any kind of…

A: Explanation we have to estimate ln(1.1) and sec(0.1) using a linear approximation method  linear…

Q: Using integration, derive the Laplace transform of: L(cosh at)

A: We will use the definition of laplace transform and concept of definite integration to derive the…

Q: dx ах VX

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Q: 3 +h (2x) dx By specifying the type of integr rol, examine it by its convegene explaining

A: We are given an improper integral of the first kind by the following.…

Q: What values of a and b maximize the value of (x – x²) dx? |(Hint: Where is the integrand positive?)

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Q: calculate the limit of ln(x) - (e)^x  x goes to + infinite

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Q: Find the absolute maximum and minimum values of ƒ(x) =10x (2 - ln x) on the interval [1, e2 ]

A: The given function is  ,fx=10x2-lnx on interval 1 , e2. To find the absolute maximum and minimum…

Q: Use the Table of Integrals on the Reference Pages toevaluate the integral.

A: To Evaluate: ∫csc5t dt Concept: i. Reduction Formula:∫cscnxdx=-1n-1cscn-2xcotx+n-2n-1∫cscn-2xdx.ii.…

Q: Integration review Evaluate the following integrals.

A: Given: ∫01t21+t6dt

Q: Determine h and N to approximate the integral e- dt within an accuracy of G = 10-5 using the (i)…

A: ii)  Equation is f(x)=exp(-x2).The value of the table for x and y x 0 0.25 0.5 0.75 1 y 1…

Q: Evaluate dx using Simpson's rule. 3

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Q: Evaluate the integral. HINT: [Use a shortcut.] e3x - 1 dx

A: Given integral: ∫-22e3x-1dx Substitute u=3x-1 and differentiate it w.r.t 'x'…

Q: Use a linear approximation (or differentials) to  estimate the given number.    cube root of 1001

A: Given: 10013 or 100113

Q: Consider the time (t) vs velocity (v) data given below. Calculate the total displacement in 12…

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Q: Use Romberg integration to approximate √² 2x² + x − 1 dx. Compute the Romberg table until Rij-…

A: The Final diagonal element is always consider the best estimate of the integral  I=∫abf(x)…

Q: LD in evaluate the intearal (Use Ć Jor the constant -6t te dt

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Q: Use a linear approximation (or differentials) to estimate the given number. (use the linearization…

A: Given function is: To find the linear approximation of f(999) we have to use the formula: With…

Q: Determine if this improper integral will diverge or converge dx (x² – 1)4/3 1 Apply this in solving:…

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Q: Em hake 3 an

A: We can find the integral as below