Suppose that TE L(V) is not nilpotent. Let n = V – null T"-1 dim V. Show that O range T"-1.

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: 1- Compare the results of the closed and open Newton-Cotes formulas when approximating a) x In x…

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

A: Given, function f(x)=cosx - 3x+1 f(0)f(π2)&lt;0hence, f(x) has root in [0,π2] We have to calculate…

Q: 3. Use the Comparison Test to determine whether the integral cos? x dx is convergent or divergent.…

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

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Q: If f(x) = –3x + sin(47x) for x E [0, 1], find the smallest value of c E (0, 1) which satisfies the…

A: The Mean Value theorem states that for a continuous and differentiable function f(x) on the interval…

Q: Given Ln = 4 + express the limit as n → ∞ as a definite integral, that is provide a, b and f(x) in…

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Q: e ax dx

A: 1. Let In=∫xneaxdx. Use the integration by parts formula ∫udv=uv-∫vdudxdx to evaluate the integral…

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

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Q: Given f (x) = |x| for x E [–n, 1] Show that 4 cos(2n – 1)x |x| = 2 E - - - (2п — 1)2 n=1

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Q: f arctan y dy 3 ¥

A: Given problem:- ∫arctan(y)/y3 dy

Q: If f(s)=sinh(s)^13 cosh(s)^10 , find f'(s)=???

A: We have  f(s)=sinh13(s)*cosh10(s)   We have to find its derivative…

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

A: The given function is               f(x)=cos x-3x+1 It is known that f(x) has a root in 0, π2. Using…

Q: What is the limit of sin when x approaches 0? Select one: O a. 1 O b. 0 O c. Does not exist

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Q: Find the value of the positive integer A so that: In A 1 sinh x dx 4 Jo

A: ∫0lnA sinhx=14 coshx0lnA=14 coshlnA-coshln1=14 coshlnA-cosh0=14 coshlnA-1=14 coshlnA=14+1…

Q: O Approximate So In (3 + sin x)dx using Simpson's Rule with(n = 4 %3D

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Q: Find cosh a In(sinh r)dr.

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Q: dy dr

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Q: 1. Rewrite the following improper integrals as a limit and then evalute them, or state that they…

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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: | 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: Show that for every 0 < p < 1 the integral 1 1 sin – dx xP is both improper and convergent.

A: Answer

Q: Apply the open Newton-Cotes formula with 3.5 xe*dx n=1 to approximate 0.5

A: For n =1 , ∆x = b-a3 , and the abscissas are x0 = a+∆x and x1 = a+2∆x . The Lagrange polynomials…

Q: From the equation, f(θ)=sinθcos2θ-(cot θ / θ) +1, what is/are the critical points?

A: Consider the equation

Q: Prove the following: d -1 arccos(x) dx V1- x2

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Q: 1)Differentiate the following f(x) = x³In (3x² – 2x + 7) e sin (x) g(x) = %3D x² – 1 h(x) = log,(x +…

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: G:2 Approximate the sel of K= Sin xo upto 4 decimal places by using Nedu'ton methed

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Q: How large should n be to guarantee that the Simpson's Rule approximation to 19e is accurate to…

A: We need to find how large should n be.

Q: Find the greatest value of F (x)= | (6 . cos t - 2 sin t) dt 5 7/3 in the interval [5/3,7 t/ 4|.

A: Fro the given problem: Fx=∫5π/3x6cost-2sintdt Now solve the above definite integral,…

Q: Show that for every 0 < p < 1 the integral 1 1 sin = dx xP is both improper and convergent.

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Q: d41 -cosh(x) at x : O is dx41

A: cosh (x)

Q: The integral S x dx x²+√√x²-1-1 can be transformed to which of the following using trigonometric…

A: Please follow the next step.

Q: Find F' if rsin ) = /" 4 nin" t t. F(x) = cos-lr

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Q: 25 3. In r If the triple integral fo So So (xe") dydr dz Find the upper limit value E.

A: We have to find the value of E.

Q: Q2. Let f(x) - In(cos x) (i) Find the are length (ds) of the function

A: Given,                f(x) = ln(cos x) ⇒y=ln(cos x) ⇒ dydx=-sin(x)cos(x). And we have to find arc…

Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+37) -dx, 1+x?

A: According to the fundamental theorem of calculus ∫x0xnf(x)dx=F(xn)-F(x0), where dFdx=f(x). The…

Q: How large should n be to guarantee that the Simpson's Rule approximation to 5(e^x^2) (bounds 1 and…

A: F is continuous on 4th derivative over the interval [a,b]. the error of integral f(x) is given by

Q: Write out Taylor's formula around 0 of degree three, f(x) = P3(x) + E3(x), for f(x) = = COs x.

A: Given that fx=cosx. To determine the Taylor's formula around 0 of degree three. That is, fx=P3x+E3x…

Q: Given +2 – 25 dt 1+ cos2(t) f(x) : At what value of x does the local max of f(x) occur? Preview

A: Consider the given function.

Q: Find F'(x) given that F(x) 3+sin (5t) dt. |3D In (t8) Provide your answer below: F'(x) =

A: The objective is to find F'(x).

Q: . Consider the function ƒ(x) = cos x − 3x + 1. Since ƒ (0)ƒ (²) < 0, ƒ(x) has a root in [o,]. If we…

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Q: Q2 ) Use the Simpson's rule with (n = 4) to estimate thef²n sinx dx . 2

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Q: Show that +2100 kT te kT = [0 – 0] = 0; t from 0 to o

A: We need to show thatkTte-t2KT0∞=[0-0]=0where t from 0 to infinity

Q: Limit as t goes to 0 of    (t^3+3t) / sin (5t)

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Q: 12) a) Use either the Trapezoid OR Midpoint Rule to estimate [ In(1+e* ) dx using at least four…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Use the Error Bound to find the least possible value of N for which Error (SN) <1 x 10 9 in…

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Q: Let f (x) = In (x?) find the equati on oE the line tangent to the graphof f at (3, In(9)) (2) Find…

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