Use the Error Bound to find the least possible value of N for which Error (SN) <1 x 10 9 in approximating L' 4e dx using the result that K,(b- a)5 Error(SN) S 180N4 where K, is the least upper bound for all absolute values of the fourth derivatives of the function 4e on the interval [a, b).

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A: Given function is  f(x)=∫21x21x3e7t2dt Since at x=1, upper limit of the integral is equal to lower…

Q: Determine the equation of the tangent line to the graph of g(x) =| [1- sin(re')] dt at the In z…

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Q: Compute the second derivative of  f(x)=ex+x  at x = 1 using a step size h = 0.1  The forward…

A: Since you have posted multiple questions. I am answering the first one. Please post the question…

Q: hi, i've added the problem as a picture please take a look. thanks in advance!

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Q: Find the firs t derivative of the f anction y=4sin[sselur)] at the Point x= T

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Q: The integral I = 66 In 1 + 2) dx is [Hint: You may need to use the Mean Value Theorem for…

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Q: dy For the function dt = 3 cos t, the third dy order derivative is dt3 -3 sin t -3 cos t 3 cos t 3…

A: Find the third derivative of the first derivative  function

Q: Compute the second derivative of  f(x)=ex+x  at x = 2 using a step size h = 0.2  The backward…

A: According to the question; f(x)=ex+x                                                     ; x=2step…

Q: Find the derivative of cos(0)d0. du Jo cos(0)de = cos (w²) · 2w • d de So" cos(8)d0 = cos(2w) • d S…

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Q: Take a look at the derivative of the integral * S (6t2 – 5t + 2) dt. (6t² dr Evaluate the…

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Q: 3. Compute the first four derivatives of f(x) = sin r + cos r. Try to find a pattern and guess the…

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Q: o find D7 and 22 by implicit diffeuentiatio Confirm that the results obtained agree with these…

A: Consider  the function fTo find: ∂z∂xWe differentiate it with respect to x, treating y as…

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Q: Q3: Find the first derivative of y= cos(x) at x= t/2 using a step size of h= Tt/12. Use forward and…

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Q: Determine the points in the interval (0, 2T) at which the graph of the function below has a…

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Q: Use forward and backward difference approximations of O(h) and a centered difference approximation…

A: Step:-1 Note:-  1. Forward difference approximation for first derivative f'x ≈fx+h-fxh 2. Backward…

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Q: Use forward and backward difference approximations of O(h) and a centered difference approximation…

A: We are given that fx=x-1-0.5sinx and we have to calculate first derivative at x=π4 with step size…

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Q: Express the limit as a definite integral on the given interval. [2 - 5(x,")2 + 6(x,)³] Ax, [4, 8] n-…

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Q: . Use the forward-difference formula to approximate the derivative of f(x)= Inx at x, =1.9 using…

A: Forward Difference: For small values of h, the difference quotient can be used to approximate with…

Q: Q5: Find for the following functions: (4) y = x sinh 2x cosh 2x (3) y = e* sin² x In√x

A: The given functions,3) y=exsin2xlnx4) y=xsinh2x-12cosh2x

Q: The equation of tangent line of the function 36 x3 f(x) e7t dt 36 х at x=1 is Oy- V36 el764 (x-1)…

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Q: Let h (x) = x sin . 1. Find the x-values where h has horizontal tangent lines in the interval 0, 27.…

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Q: Find an equation of the tangent line to the graph of f(x) = | t cosh (t² – 1) dt tan-lt 1+In (x) at…

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Q: Find dw/ds and dw/dt using the appropriate Chain Rule. Function Values w = sin(4x + 5y) x-s+t, y =…

A: The given function,w=sin(4x+5y)x=s+ty=s-tat the point s=0, t=π2

Q: Evaluate the second derivative of mq4.5.png os (bVx³) f(x) = a ln sin(cx2) if a = 21, b = 0.5, and c…

A: Given that, f(x)=alncosbx3sincx2a=21, b=0.5, c=5Substituting the values of a, b and c, we…

Q: Find the differential of each function. (a) y = etan(nt) tan(at) · soc2 (at) - T dy = sec“(at) · T e…

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Q: Determine the equation of the tangent line to the graph of g(x) = | [1- sin(re')] dt at the /In x…

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Q: 1. Find the derivative of the following functions (dy/dx) at x=Tt/4 cos x2 1– sin x2 y= 2. Find the…

A: We have to find the derivatives of given function at x=π/4  1. y= cosx2/(1-sinx2) 2. y=x3sin3xcos3x

Q: 22. Detemine whether the improper integral converges or diverges, and if it converges, find its…

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Q: Use a summation to find the integral from 0 to 4 of f(x) 2x + 1.  Then check it using the power rule…

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Q: Compute the derivative of g(x) = cos(t²) dt. O 42 sin(z*) O cos(x*) -42 sin(z*) O 4a cos(a) O -…

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Q: Q6:- Show that R = (sin t)i + (cos t)j + v3k has a constant length. And R(t) is orthogonal to its…

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

Q: Find the derivative. cos X d 78° dt dx 1 a. by evaluating the integral and differentiating the…

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Q: Determine the equation of the tangent line to the graph of g(x) = Sm, [1 – sin(ne')]dt at %3D In x…

A: We have to find the equation of the tangent line to the graph of gx=∫lnx01-sinπetdt at the point…

Q: 55. Show that dx J+4 converges by comparing with x³ + xdx. -3 dx. х

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Q: Compute forward difference approximations for the first derivative of the function, y = e*cos(x²),…

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Q: Find the slope of the tangent line to the graph of f(x) 2e'cos-1t dt at x = 1. In x = X'

A: Find the slope with the help of derivative of f(x) at x=1 .

Q: F(x) = x · S, 2e' cos-lt dt at x = 1 In x

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Q: Find an equation of the tangent line to the graph of {(=) = [. t cosh (t² – 1) dt f(x) /1+ln (x)…

A: First I have written the rule of derivative of an integral to find the slope of tangent line for…

Q: 2) Find second derivative d'F/dt? of 312-2 F? = 13 and find it at (t,F) = (-1,2)

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Q: Compute the first, second, and third derivatives of r(t) = 9ti + 5 In(t)j + 5e-3tk. first derivative…

A: As we know that; The Sum/Difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 The Chain rule:…

Q: (a) Explain why | dr is divergent. (b) Find all value(s) of t > 0 for which the integral / 1 dx is…

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Q: Find the actual error when the first derivative of f(x) = sin(2x) at *=1/8 s approximated by the…

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

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Q: Does fn converges to L1 and L2 i.e the distance between fn and f goes to 0

A: By the theorem: A metric  on BE is the uniform metric du  . A sequence of bounded functions fn:E→ℝ…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.